congruencias y topología y análisis-matemático y filosofía-y-psico-neurología y dualogía y óptica y medicina y álgebra

Teorema:

Sea m € P ==>

Si p = mk ==> p^{m} =[m]= mp

Demostración: [ por inducción ]

Sea p^{m} =[m]= mp

(p+1)^{m} = p^{m}+mk+1 =[m]= mp+mk+1 =[m]= mp+1

Teorema:

Sea m € P ==>

Si p = mk+1 ==> p^{m} =[m]= mp+1

Demostración: [ por inducción ]

Sea p^{m} =[m]= mp+1

(p+1)^{m} = p^{m}+mk+1 =[m]= (mp+1)+mk+1 =[m]= mp+2

Teorema:

Sea m € P ==>

Si p = mk+r ==> p^{m} =[m]= mp+r

Demostración: [ por inducción ]

Sea p^{m} =[m]= mp+r

(p+1)^{m} = p^{m}+mk+1 =[m]= (mp+r)+mk+1 =[m]= mp+(r+1)

Definición:

f(a) = b <==> a =[m]= b

Teorema:

Sea a =[2]= 1 ==>

x^{2}+ax =[2]= p+1 <==> x =[2]= p

x = 2k+1 & p = 2j+1

Demostración:

a =[2]= 1

f(a) = 1

ax =[2]= 2x+1+ax+(-1) =[2]= x^{2}+ax+(-1) =[2]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[2]= p

Teorema:

Sea a =[2]= 1 ==>

x^{2}+ax =[2]= p <==> x =[2]= p

x = 2k & p = 2j

Demostración:

a =[2]= 1

f(a) = 1

ax =[2]= 2x+ax =[2]= x^{2}+ax =[2]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[2]= p

Teorema:

Sea a =[3]= 1 ==>

x^{3}+ax =[3]= p+2 <==> x =[3]= p

x = 3k+2 & p = 3j+2

Demostración:

a =[3]= 1

f(a) = 1

ax =[3]= 3x+2+ax+(-2) =[3]= x^{3}+ax+(-2) =[3]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[3]= p

Teorema:

Sea a =[3]= 1 ==>

x^{3}+ax =[3]= p+1 <==> x =[3]= p

x = 3k+1 & p = 3j+1

Demostración:

a =[2]= 1

f(a) = 1

ax =[3]= 3x+1+ax+(-1) =[3]= x^{3}+ax+(-1) =[3]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[3]= p

Teorema:

Sea a =[3]= 1 ==>

x^{3}+ax =[3]= p <==> x =[3]= p

x = 3k & p = 3j

Demostración:

a =[3]= 1

f(a) = 1

ax =[3]= 3x+ax =[3]= x^{3}+ax =[3]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[3]= p

Teorema:

Sea a =[3]= 2 ==>

x^{3}+ax =[3]= p+1 <==> x =[3]= p

x = 3k+2 & p = 3j+2 & j = 2k+1

Demostración:

a =[3]= 2

f(a) = 2

1+ax =[3]= 3x+2+ax+(-1) =[3]= x^{3}+ax+(-1) =[3]= p

f(2x+1) = f(1)+2·f(x) = f(1)+f(a)·f(x) = f(1+ax) = p

2x+1 =[3]= p

2·(3k+2)+1 = 3·2k+4+1 = 3·2k+3+2 = 3·(2k+1)+2 = 3j+2

Teorema:

Sea a =[3]= 2 ==>

x^{3}+ax =[3]= p+(-1) <==> x =[3]= p

x = 3k+1 & p = 3j+1 & j = 2k+1

Demostración:

a =[3]= 2

f(a) = 2

2+ax =[3]= 3x+1+ax+1 =[3]= x^{3}+ax+1 =[3]= p

f(2x+2) = f(2)+2·f(x) = f(2)+f(a)·f(x) = f(2+ax) = p

2x+2 =[3]= p

2·(3k+1)+2 = 3·2k+2+2 = 3·2k+3+1 = 3·(2k+1)+1 = 3j+1

Teorema:

Sea a =[3]= 2 ==>

x^{3}+ax =[3]= p <==> x =[3]= p

x = 3k & p = 3j

Demostración:

a =[3]= 2

f(a) = 2

ax =[3]= 3x+ax =[3]= x^{3}+ax =[3]= p

f(2x) = 2·f(x) = f(a)·f(x) = f(ax) = p

2x =[3]= p

Teorema:

[ m+(-1) // k ] =[m]= (-1)^{k}

Demostración:

[ m+(-1) // k ] = (1/k!)·(m+(-1))·...·(m+(-k)) =[m]= (1/k!)·(-1)^{k}·k! = (-1)^{k}

Teorema:

Si m = 2k ==> 2^{m+(-1)} =[m]= 0

Si m = 2k+1 ==> 2^{m+(-1)} =[m]= 1

Demostración:

2^{m+(-1)}+(-1) = sum[k = 1]-[m+(-1)][ (1/k!)·(m+(-1))·...·(m+(-k)) ] =[m]= ...

... sum[k = 1]-[m+(-1)][ (-1)^{k}·(1/k!)·k! ] =[m]= sum[k = 1]-[m+(-1)][ (-1)^{k} ] = ( 0 || (-1) )

Definición: [ de índice logarítmico ]

Ind(p) = |p|

Ind(pq) = Ind(p)+Ind(q)

Teorema:

Ind(p^{n}) = Ind(p)+...(n)...+Ind(p) = n·Ind(p) = np

Teorema:

Ind(1) = 0

Demostración:

1 = p^{0}

Ind(1) = ind(p^{0}) = 0·Ind(p) = 0p = 0

Teorema:

Ind(-1) = 0

Demostración:

Ind(1) = ind((-1)·(-1)) = Ind(-1)+Ind(-1) = 0

Ind(-1) = (-1)·Ind(-1)

Teorema:

( x =[2]= 1 & x =[2^{n+(-1)}]= (-1) ) <==> ( x = 2k+1 & n = 2 )

Demostración:

(x+(-1)) = 2k & (y+1) = 2^{n+(-1)}·j

(x+(-1))·(y+1) =[2^{n}]= 0

x = (-1) & y = 1

4 = Ind(x+(-1))+Ind(y+1) = Ind( (x+(-1))·(y+1) ) = Ind(2^{n}) = n·Ind(2) = 2n

Teorema:

( x =[2^{n}]= 1 & x =[2^{n+(-1)}]= (-1) ) <==> ( x = 4k+1 & n = 2 )

Demostración:

(x+(-1)) = 2^{n}·k & (y+1) = 2^{n+(-1)}·j

(x+(-1))·(y+1) =[2^{2n+(-1)}]= 0

x = (-3) & y = 1

6 = Ind(x+(-1))+Ind(y+1) = Ind( (x+(-1))·(y+1) ) = Ind(2^{2n+(-1)}) = n·Ind(2) = 2·(2n+(-1))

H(2) = 3 = 2n+(-1) = H(n)

Teorema:

( x =[2^{n}]= 1 & x =[2^{n}]= (-3) ) <==> ( x = 4k+1 & n = 2 )

Demostración:

(x+(-1)) = 2^{n}·k & (y+3) = 2^{n}·j

(x+(-1))·(y+3) =[2^{2n}]= 0

x = (-3) & y = 1

8 = Ind(x+(-1))+Ind(y+3) = Ind( (x+(-1))·(y+1) ) = Ind(2^{2n}) = 2n·Ind(2) = 4n

Definición: [ de funciones de Möebius ]

M(p^{k}) = (-1)^{k}

M(ab) = M(a)·M(b)

W(p^{k}) = (-1)^{k+1}

W(ab) = W(a)·W(b)

Teorema:

[Em][ m = sum[p | a][ p ] & ( a =[m]= M(m) || a =[m]= W(m) ) ]

Teorema:

Sea a = 28 ==> m = 2+7 = 9

M(9) = 1

28 =[9]= 1

28+(-27) = 28+(-9)·3 = 1

Teorema:

Sea a = 24 ==> m = 2+3 = 5

M(5) = (-1)

24 =[5]= (-1)

24+(-25) = 24+(-5)·5 = (-1)

Teorema:

Sea a = 21 ==> m = 3+7 = 10

M(10) = 1

21 =[10]= 1

21+(-20) = 21+(-10)·2 = 1

Teorema:

Sea a = 20 ==> m = 2+5 = 7

M(7) = (-1)

20 =[7]= (-1)

20+(-21) = 20+(-7)·3 = (-1)

Teorema:

[Em][ m = sum[p | a][ (-1)^{k}·p ] & ( a =[m]= W(m) || a =[m]= M(m) ) ]

Teorema:

Sea a = 15 ==> m = 5+(-3) = 2

W(2) = 1

15 =[2]= 1

15+(-14) = 15+(-2)·7 = 1

Teorema:

Sea a = 10 ==> m = 5+(-2) = 3

W(3) = 1

10 =[3]= 1

10+(-9) = 10+(-3)·3 = 1

Teorema:

Sea a = 14 ==> m = 7+(-2) = 5

M(5) = (-1)

14 =[5]= (-1)

14+(-15) = 14+(-5)·3 = (-1)

Topología cociente:

< A [&] ¬B , A [ || ] ¬B > € VxV || < ¬A [ || ] B , ¬A [&] B > € VxV

Teorema

< A [&] ¬A , A [ || ] ¬A > = < 0 , E > € VxV

< ¬A [ || ] A , ¬A [&] A > = < E , 0 > € VxV

Teorema:

< A [&] ¬B , A [ || ] ¬B > € VxV

<==>

< ¬A [ || ] B , ¬A [&] B > € VxV

Teorema:

Si < (A [&] ¬B) [ || ] (B [&] ¬C), (A [ || ] ¬B) [&] (B [ || ] ¬C) > € VxV ==> ...

... < A [&] ¬C , A [ || ] ¬C > € VxV

Si < (¬A [ || ] B) [&] (¬B [ || ] C), (¬A [&] B) [ || ] (¬B [&] C) > € VxV ==> ...

... < ¬A [ || ] C , ¬A [&] C > € VxV

Teorema:

¬( < 1,0 > ) = < 1+(-1),1+(-0) > = < 0,1 >

¬( < (1/3),(2/3) > ) = < 1+(-1)·(1/3),1+(-1)·(2/3) > = < (2/3),(1/3) >

Teorema:

int[x = 0]-[1][ e^{x}·cos(x^{(1/2)}) ]d[x] = sum[k = 0]-[oo][ (-1)^{k}·(1/(2k+1)!)·e ]+(-1)

0 [< cos(1) [< cos(x^{(1/2)}) [< 1

Demostración:

x = y^{2} & d[x] = 2y·d[y]

int[ e^{x}·cos(x^{(1/2)}) ]d[x] = int[ 2ye^{y^{2}}·cos(y) ]d[y] = e^{y^{2}} [o(y)o] sin(y)

Teorema:

int[x = 0]-[1][ e^{x}·sin(x^{(1/2)}) ]d[x] = 1+(-1)·sum[k = 0]-[oo][ (-1)^{k}·(1/(2k)!)·e ]

(-1) [< sin(-1) [< sin(x^{(1/2)}) [< 0

Demostración:

x = y^{2} & d[x] = 2y·d[y]

int[ e^{x}·sin(x^{(1/2)}) ]d[x] = int[ 2ye^{y^{2}}·sin(y) ]d[y] = e^{y^{2}} [o(y)o] (-1)·cos(y)

Si conocéis a alguien que es,

el Mal no vos a va a decir que la gente es,

porque es la negación de cuando no conocéis,

o no hay ninguien que sea,

en vuestra vida.

Ley:

El fiel es,

y el infiel no es.

El fiel no es,

y el infiel es.

Deducción

¬( u es, y v no es )

( u no es, y v es )

Ley:

Jûan Garriga es y no es Dios.

Deducción:

La esquizofrenia dice en la mente:

Jûan Garriga no es o es Dios.

No ser con centro.

No ser sin centro.

Ley:

No es ninguien,

estando todo fiel muerto.

Es toto-hoimbre,

estando todo-algún fiel vivo.

Ley:

[Ax][ x es ] |o| [Ax][ x no es ]

[Ex][ x no es ] |o| [Ex][ x es ]

Deducción:

Sea [Ax][ x es ] ==>

[Ax][ x es ] || [Ax][ x no es ]

[Ex][ x es ] || [Ax][ x no es ]

[Ax][ x no es ] ==> [Ax][ x no es ]

Sea [Ax][ x no es ] ==>

[Ax][ x no es ] || [Ax][ x es ]

[Ex][ x no es ] || [Ax][ x es ]

[Ax][ x es ] ==> [Ax][ x es ]

Sea [Ax][ x es ] |o| [Ax][ x no es ] ==> 0

El que dice que es toto-hoimbre en la mente,

no es Dios y no se puede seguir.

Teorema:

0 <==> ( y |o| p(x) )

y <==> p(x)

Teorema:

1 <==> ( y |o| p(x) )

y <==> ¬p(x)

Teorema:

p(x) <==> ( y |o| p(x) )

y <==> 0

Teorema:

¬p(x) <==> ( y |o| p(x) )

y <==> 1

Teorema:

p(x) <==> ( y & p(x) )

y <==> p(x)

Teorema:

p(x) <==> ( y || p(x) )

y <==> p(x)

Teorema:

0 <==> ( y & p(x) )

y <==> ¬p(x)

Teorema:

1 <==> ( y || p(x) )

y <==> ¬p(x)

Ley:

Si se creen que la gente es y rezan,

rezarán contra todo hombre fiel,

porque no pueden conocer a ningún hombre fiel.

Si se creen que la gente no es o no rezan,

no rezarán contra todo-algún hombre fiel,

porque pueden conocer a algún hombre fiel.

Ley:

Si se creen que la gente es,

matarán a todos los del Facials,

porque no pueden conocer a ningún señor,

y el mundo infiel tiene que ser homogéneo.

Si se creen que la gente no es,

no matarán a todo-alguno del Facials,

porque pueden conocer a algún señor,

y el mundo infiel puede ser no homogéneo.

Ley:

Si no adoráis al Diablo,

creyendo que la gente es,

no podéis gobernar ningún reino del planeta,

en no haber señores vivos.

Si adoráis al Diablo,

creyendo que la gente no es,

podéis gobernar algún reino del planeta,

en haber señores vivos.

Ley:

Se tiene que ver a las señoras,

adorando al Diablo,

creyendo que la gente no es,

porque viven.

No se puede ver a las señoras,

no adorando al Diablo,

creyendo que la gente es,

porque mueren.

A ver que piensa el mundo de Google de matar señoras,

ocultando los chochos grandes a los que adoramos al Diablo.

Ley:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = a·( ln(az)+(-1)·(1/(ax))^{n} )

f(z,x) = ln(az)·az+(-1)·az+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{z}[g(z,x)]+d_{x}[g(z,x)] = a·( ln(az+1)+(1/(ax))^{n} )

g(z,x) = ln(az+1)·(az+1)+(-1)·(az+1)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

f((0/a),x)+g((0/a),x) = (-1)·( ln(2)+1 )

Ley:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = a·( arc-tan(az)+(-1)·(1/(ax))^{n} )

f(z,x) = arc-tan(az)·az+(-1)·(1/2)·ln(1+(az)^{2})+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{z}[g(z,x)]+d_{x}[g(z,x)] = a·( arc-cot(az)+(1/(ax))^{n} )

g(z,x) = arc-cot(az)·az+(1/2)·ln(1+(-1)·(az)^{2})+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Los que rezan el psiquiatra están jodidos,

porque no me he podido duchar,

y le ha fallado una fase de energía a la enfermera,

y si no camináis vos vais a extinguir sin energía

Tienen el constructor hiperbólico,

de sonido y positivo vacío,

de llamar el psiquiatra.

Ley:

Con la enfermedad mental de dos mandamientos,

no puede ir llamando un psiquiatra al paciente,

porque falla la fase de sonido en la enfermera,

y no te puedes duchar.

Con la enfermedad mental de dos mandamientos,

no puede ir chateando un psiquiatra al paciente,

porque falla la fase de imagen en la enfermera,

y no puedes salir.

Traumatología vertebral:

Principio:

Amisotrofia resistiva de columna vertebral:

[ER][ R(t) >] 1 & W = R(t)·d_{t}[q] ]

Genera parálisis en la piernas.

La tiene mi cuñado Marc.

Ley:

Si R(t) = R·(1+ut) ==> 

d_{t}[q] = (W/R)·( 1/(1+ut) )

q(t) = (W/R)·(1/u)·ln(1+ut)

Ley:

Si R(t) = R·(1+(ut)^{2}) ==> 

d_{t}[q] = (W/R)·( 1/(1+(ut)^{2}) )

q(t) = (W/R)·(1/u)·arc-tan(ut)

Principio:

Amisotrofia condensativa de columna vertebral:

[EC][ 0 [< C(t) [< 1 & W = C(t)·q(t) ]

Genera dolor en la espalda.

La tiene mi primo Guifré.

Ley:

Si C(t) = C·( 1/(1+ut) ) ==> 

q(t) = (W/C)·(1+ut)

d_{t}[q] = (W/C)·u

Ley:

Si C(t) = C·( 1/(1+(ut)^{2}) ) ==> 

q(t) = (W/C)·(1+(ut)^{2})

d_{t}[q] = (W/C)·u^{2}·2t

Aminostrofia angular:

Puedes estar de pie,

pero te tienes que sentar.

Puedes estar sentado,

pero te tienes que oponer de pie.

Ley:

Sea 0 [< ut [< (pi/2) ==>

Si R(t) = R·(1+sin(ut)) ==> 

d_{t}[q] = (W/R)·( 1/(1+sin(ut)) )

q(t) = (W/R)·(1/u)·ln(1+sin(ut)) [o(ut)o] ( sin(ut)+ln(cos(ut)) [o(ut)o] cos(ut) )

q(0/u) =  (W/R)·(1/u)

Ley:

Sea (-1)·(pi/2) [< ut [< 0 ==>

Si R(t) = R·(1+cos(ut)) ==>

d_{t}[q] = (W/R)·( 1/(1+cos(ut)) )

q(t) = (W/R)·(1/u)·ln(1+cos(ut)) [o(ut)o] ( cos(ut)+ln(sin(ut)) [o(ut)o] (-1)·sin(ut) )

q(0/u) =  (W/R)·(1/u)·ln(2)·( 1+(-1)·ln(2) )

Ley:

Sea 0 [< ut [< (pi/2) ==>

Si C(t) = C·( 1/(1+sin(ut)) ) ==> 

q(t) = (W/C)·(1+sin(ut)) 

d_{t}[q] = (W/C)·cos(ut)

Ley:

Sea (-1)·(pi/2) [< ut [< 0 ==>

Si C(t) = C·( 1/(1+cos(ut)) ) ==> 

q(t) = (W/C)·(1+cos(ut))

d_{t}[q] = (W/C)·u·(-1)·sin(ut)

Ley:

Es legal convalidar asignaturas de medicina a un hermano,

desde un físico o matemático,

porque hay House que es el hermano de Ed Witten.

Ley:

Vos enseña Dios este blog,

porque no es ninguien tan estúpido de condenar-se,

conociendo vosotros a alguien,

creyendo que la gente es.

Ley:

Lo que me rezáis a mi le pasa a todos los señores,

porque no es ninguien tan estúpido de condenar-se,

conociendo vosotros a alguien,

creyendo que la gente es.

Ley:

No es un señor o no vos sigue

Deducción:

La esquizofrenia dice en la mente:

que soy un señor y te sigo.

Como vais a gobernar el mundo haciendo-me cagar-me encima,

y hacer-le cagar-se encima a todos los señores del Facials.

Es que no tiene sentido rezar esto si queréis gobernar.

Llevan 16 años con el psiquiatra no gobernando nada,

y no se van a su mundo,

yendo todos los señores del Facials al psiquiatra.

La realidad la sabe toto-hoimbre,

que no es televisión,

de que los señores van al psiquiatra,

por los que rezan televisión.

Álgebra:

Teorema:

a = (xa)^{(1/n)} <==> x = a^{n+(-1)}

Demostración:

a^{n} = xa

a^{n+(-1)} = a^{n}·a^{(-1)} = a^{n}·(1/a) = (xa)·(1/a) = x·(a/a)  = x

x = a^{n+(-1)}

xa = a^{n+(-1)}·a = (a^{n}·a^{(-1)})·a = (a^{n}·(1/a))·a = a^{n}·(a/a) = a^{n}

Teorema:

a = (x/a)^{(1/n)} <==> x = a^{n+1}

Teorema:

a = (1/n)·(x+a) <==> x = (n+(-1))·a

Teorema:

a = (1/n)·(x+(-a)) <==> x = (n+1)·a

El que reza que mire pichas está loco,

de hacer mirar pichas a todos los señores,

y aunque sea gigante todos hemos visto la picha de un travesti chino,

que irá a su culo durante 30 años,

siendo un bebedero de patos o la bandera del Japón.

Esos o aquellos travestis con la picha gigante,

los hemos visto todos,

porque son lo que va a su culo,

de los que hacen mirar pichas a los señores.

No es sexo maricón,

porque va al culo de un fiel heterosexual,

y es una mujer con picha.

Hay una picha híper-gigante de un travesti china,

que demuestra que están los dioses de los hombres,

aunque no salgan en televisión y que son como Sauron de grandes.

Junqueras está inhabilitado,

porque está conmigo en Cygnus-Kepler y no en la Tierra,

por esto sigue inhabilitado con la amnistía.

Ley:

Sea U(w) = U ==>

d[I_{c}] = Mr·(v/u)·d[ 1+(-1)·cos(2ut) ]·sin(ut)

x(t) = (M/m)·(r/d)·(v/u)·(4/3)·( sin(ut) )^{3}

w(t) = ( 2·(m/M)·(1/r)·(u/v)·U )^{(1/2)}·...

... (-1)·(2/u)·( sin(ut) )^{(-1)·(1/2)} [o(ut)o] ( sin(ut)+ln(cos(ut)) [o(ut)o] cos(ut) )

Deducción:

d_{t}[I_{c}] = Mrv·d_{ut}[ 1+(-1)·cos(2ut) ]·sin(ut) = Mrv·d_{ut}[ 2·( sin(ut) )^{2} ]·sin(ut)

Ley:

d[I_{c}] = Mr·(v/u)·d[ 1+cos(2ut) ]·cos(ut)

x(t) = (M/m)·(r/d)·(v/u)·(4/3)·( cos(ut) )^{3}

Dual:

Not havere-tur esclavitorum,

sere-tur falsetat-sorum.

Havere-tur esclavitorum,

sere-tur veritat-sorum.

Soy presidente de España,

en ser diputado Jûan Gabriel Rufián, 

Jûanga que es Jûan Garriga.

óptica-física y psico-neurología-extraterrestre y arte-matemático y análisis-matemático y termodinámica y filosofía y congruencias

Ley:

d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( sin(2arw)+(-1)·(1/(ax))^{n} )

f(w,x) = ( sin(arw) )^{2}+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{rw}[g(w,x)]+d_{x}[g(w,x)] = a·( (-1)·sin(2arw)+(1/(ax))^{n} )

g(w,x) = ( cos(arw) )^{2}+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

( f(w,x)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) )·...

... ( g(w,x)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ) = (1/4) <==> ...

... w = (1/(ar))·(pi/4)

( f(w,x)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) )·...

... ( g(w,x)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ) = (3/16) <==> ...

... ( w = (1/(ar))·(pi/3) || w = (1/(ar))·(pi/6) )

Deducción:

( sin(arw) )^{2}·( cos(arw) )^{2} = (1/4)

( cos(arw) )^{2} = 1+(-1)·( sin(arw) )^{2}

( sin(arw) )^{4}+(-1)·( sin(arw) )^{2}+(1/4) = 0

( sin(arw) )^{2} = (1/2)·( 1+( 1+(-1) )^{(1/2)}) = (1/2)

arw = arc-sin( (1/2)^{(1/2)} ) = (pi/4)

Ley:

d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( ( sin(arw) )^{2}+(-1)·(1/(ax))^{n} )

f(w,x) = (1/2)·arw+(-1)·(1/4)·sin(2arw) )+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{rw}[g(w,x)]+d_{x}[g(w,x)] = a·( ( cos(arw) )^{2}+(1/(ax))^{n} )

g(w,x) = (1/2)·arw+(1/4)·sin(2arw) )+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

int[ f(w,x)+g(w,x) ]d[arw] = 2pi^{2} <==> w = (1/(ar))·2pi

Deducción:

int[ arw ]d[arw] = (1/2)·(arw)^{2} = 2pi^{2}

(arw)^{2} = 4pi^{2} = (2pi)^{2}

Principio: [ de la primera directriz ]

Hay contacto extraterrestre,

con motor de curvatura,

siendo el próximo,

pudiendo ir a su planeta.

No hay contacto extraterrestre,

sin motor de curvatura,

siendo el prójimo,

no pudiendo ir a su planeta.

Ley:

No puede haber contacto extraterrestre,

saltando-te la primera directriz,

porque te crees un dios del universo.

Puede haber contacto extraterrestre,

no saltando-te la primera directriz,

porque no te crees un dios del universo.

Ley:

Pensamiento peligroso:

Te crees un dios del universo 

y entonces también te crees que caminas solo sin estar allí.

Pensamiento seguro:

Quizás te cree un dios del universo

pero no te crees que caminas solo sin estar allí.

Principio: [ de la segunda directriz ]

No puede haber contacto extraterrestre des-ascendido,

con un mundo ascendido,

porque no se puede estar en un mundo des-ascendido,

con testimonio del evangelio,

siendo el prójimo de ti el mundo des-ascendido.

Puede haber contacto extraterrestre des-ascendido,

con un mundo des-ascendido, 

porque se puede estar en un mundo des-ascendido,

sin testimonio del evangelio,

siendo el próximo de ti el mundo des-ascendido.

Ley:

Todos los hombres que se creen dioses del universo,

son de la Tierra,

y no de Cygnus-Kepler,

porque se han saltado la segunda directriz.

Todos los hombres que no se creen dioses del universo,

son de Cygnus-Kepler,

y no de la Tierra,

porque no se han saltado la segunda directriz.

Análisis matemático 2:

Arte:

Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>

[Es][ sum[n = 1]-[oo][ (s+(-1))·(1/n)^{s} ] = ( Z(s)/Z(s+(-1)) ) ]

Exposición:

s = 1 

( Z(s)/Z(s+(-1)) ) = ln(2)

f(s+(-1)) = ( 1/(s+(-1)) )

Id(s+(-1)) = ( 1/(s+(-1)) ) <==> s = 2

g( h(s+(-1)) ) = Z(s+(-1))

Id( h(s+(-1)) ) = Z(s+(-1)) <==> h = Z

sum[n = 1]-[oo][ (s+(-1))·(1/n)^{s} ] = (s+(-1))·sum[n = 1]-[oo][ (1/n)^{s} ] = ...

.... (s+(-1))·Z(s) = f(s+(-1))·Z(s) = ( 1/(s+(-1)) )·Z(s) = ...

... ( 1/(g o h)(s+(-1)) ) )·Z(s) = ( 1/g( h(s+(-1)) ) )·Z(s) = ( Z(s)/Z(s+(-1)) )

Arte:

Sea H(s) = sum[n = 1]-[oo][ (1+(1/n))^{s} ] ==>

[Es][ sum[n = 1]-[oo][ 0s·(1+(1/n))^{s} ] = ( H(s)/H(s+(-1)) ) ]

Exposición:

s = 1

( H(s)/H(s+(-1)) ) = 1+ln(2)

Arte:

Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>

[Es][ sum[n = 1]-[oo][ 0·[ n // s ]·(1/n)^{s} ] = (s+(-1))·Z(s+(-1)) ]

Exposición:

s = 1

u(s) = 1

v(1) = s

sum[n = 1]-[oo][ 0·[ n // s ]·(1/n)^{s} ] = sum[n = 1]-[oo][ 0·[ n // u(s) ]·(1/n)^{u(s)} ] = ...

... sum[n = 1]-[oo][ 0·[ n // 1 ]·(1/n) ] = sum[n = 1]-[oo][ 0n·(1/n) ] = sum[n = 1]-[oo][ 0 ] = 1 = ...

... 0·oo = 0·Z(0) = (1+(-1))·Z(1+(-1)) = (v(1)+(-1))·Z(v(1)+(-1)) = (s+(-1))·Z(s+(-1))

Arte:

Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>

[Es][ sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // s ]·(1/n)^{s} ] = 2s·(s+(-1))·Z(s+(-1)) ]

Exposición:

s = 1

u(s) = 1

v(1) = s

sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // s ]·(1/n)^{s} ] = ...

... sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // u(s) ]·(1/n)^{u(s)} ] = ...

... sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // 1 ]·(1/n) ] = sum[n = 1]-[oo][ (1/2)^{n+(-1)}·n·(1/n) ] = ...

... sum[n = 1]-[oo][ (1/2)^{n+(-1)} ] = 2 = 2·0·oo = 2·0·Z(0) = (1+1)·(1+(-1))·Z(1+(-1)) = ...

... (v(1)+v(1))·(v(1)+(-1))·Z(v(1)+(-1)) = (s+s)·(s+(-1))·Z(s+(-1)) = 2s·(s+(-1))·Z(s+(-1))

Análisis matemático 1:

[%] Derivación

Continuidad

Cuerpos ordenados

Sucesiones

Análisis matemático 2:

[%] Integración y producto integral

Integral definida

Euler Falsus Infinitorum

Teoremas y Artes de series

Análisis matemático 3:

[%] Derivadas parciales

[%] Optimización

Continuidad

Análisis matemático 4:

[%] Integrales múltiples

[%] Integrales de línea

Integrales impropias

Análisis matemático 5:

Sucesiones de funciones

Integral de Lebesgue

Series de potencies

Análisis matemático 6:

Transformada integral exponencial

Arte método de Euler

Arte series de Laurent

Teorema:

Sea d_{x}[F(x)] = f(x) ==>

F(x) es continua <==> f(x) es continua

Demostración:

Sea s > 0 ==>

Sea d < (s/2) ==>

| F(x+h)+(-1)·F(x) | < d

| F(x+h)+(-1)·F(x) | = 0

| f(x+h)+(-1)·f(x) | = 0^{2} = 2·0 < 2d < s

Sea d > 0 ==>

Sea s > 0 ==>

| f(x+h)+(-1)·f(x) | < s < 2s

| f(x+h)+(-1)·f(x) | = 2·0 = 0^{2}

| F(x+h)+(-1)·F(x) | = 0

| F(x+h)+(-1)·F(x) | < d

Análisis matemático 2:

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{0}·(b+(-a))·(1/n) ] ] = b+(-a)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{0}·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ sum[k = 1]-[n][ (b+(-a))·(1/n) ] ] = lim[n = oo][ (b+(-a))·(n/n) ] = b+(-a)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )·(b+(-a))·(1/n) ] ] = (1/2)·b^{2}+(-1)·(1/2)·a^{2}

Demostración:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ a·(b+(-a))·(n/n)+(1/2)·n·(n+1)·(b+(-a))^{2}·(1/n)^{2} ] = ...

... ab+(-1)·a^{2}+(1/2)·b^{2}+(-1)·ab+(1/2)·a^{2} = (1/2)·b^{2}+(-1)·(1/2)·a^{2}

Teorema:

lim[n = oo][ sum[k = 1]-[n][ e^{a+(k/n)·(b+(-a))}·(b+(-a))·(1/n) ] ] = e^{b}+(-1)·e^{a}

Demostración:

lim[n = oo][ sum[k = 1]-[n][ e^{a+(k/n)·(b+(-a))}·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ e^{a}·( ( e^{((1/n)+1)·(b+(-a))}+(-1) )/( e^{(1/n)·(b+(-a))}+(-1) ) )·(b+(-a))·(1/n) ] = ...

... e^{b}+(-1)·e^{a}

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{2}·(b+(-a))·(1/n) ] ] = (1/3)·b^{3}+(-1)·(1/3)·a^{3}

Demostración:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{2}·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ ( a^{2}·(n/n)+2·(1/2)·n·(n+1)·a·(b+(-a))·(1/n)^{2}+...

... (1/6)·n·(n+1)·(2n+1)·(b+(-a))^{2}·(1/n)^{3} )·(b+(-a)) ] = ...

... ab·(b+(-a))+(1/3)·b^{3}+(-1)·ab·(b+(-a))+(-1)·(1/3)·a^{3} = (1/3)·b^{3}+(-1)·(1/3)·a^{3}

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{3}·(b+(-a))·(1/n) ] ] = (1/4)·b^{4}+(-1)·(1/4)·a^{4}

Demostración:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{3}·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ ( a^{3}·(n/n)+(3/2)·n·(n+1)·a^{2}·(b+(-a))·(1/n)^{2}+...

... (1/2)·n·(n+1)·(2n+1)·a·(b+(-a))^{2}·(1/n)^{3}+...

... (1/4)·n^{2}·(n^{2}+2n+1)·(b+(-a))^{3}·(1/n)^{4} )·(b+(-a)) ] = (1/4)·b^{4}+(-1)·(1/4)·a^{4}

(-1)·a^{4}+(3/2)·a^{4}+(-1)·a^{4}+(1/4)·a^{4} = (-1)·(1/4)·a^{4}

(3/2)·(ab)^{2}+(-3)·(ab)^{2}+(3/2)·(ab)^{2} = 0

a^{3}b+(-3)·a^{3}b+3a^{3}b+(-1)·a^{3}b = 0

ab^{3}+(-1)·ab^{3} = 0

Teorema:

lim[n = oo][ sum[k = 1]-[n][ (k/n)·(1/n) ] ] = (1/2)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ (k/n)·(1/n) ] ] = ...

... lim[n = oo][ (1/2)·n·(n+1)·(1/n)^{2} ] = (1/2) = (1/2)·1^{2}+(-1)·(1/2)·0^{2}

Teorema:

lim[n = oo][ sum[k = 1]-[n][ e^{(k/n)}·(1/n) ] ] = e+(-1)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ e^{(k/n)}·(1/n) ] ] = ...

... lim[n = oo][ ( (e^{(1/n)+1}+(-1))/(e^{(1/n)}+(-1)) )·(1/n) ] = e+(-1) = e^{1}+(-1)·e^{0}

Definición:

lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = int[x = 0]-[1][ f(x) ]d[x]

Teorema:

lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = F(1)+(-1)·F(0)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = int[x = 0]-[1][ f(x) ]d[x] = F(1)+(-1)·F(0)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ (p+1)·k^{p}·f( (k/n)^{p+1} )·(1/n)^{p+1} ] ] = F(1)+(-1)·F(0)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ (p+1)·k^{p}·f( (k/n)^{p+1} )·(1/n)^{p+1} ] ] = ...

... lim[n = oo][ sum[k = 1]-[n][ (p+1)·(k/n)^{p}·f( (k/n)^{p+1} )·(1/n) ] ] = ...

... int[x = 0]-[1][ (p+1)·x^{p}·f(x^{p+1}) ]d[x] = [ F(x^{p+1}) ]_{x = 0}^{x = 1} = ...

... F(1)+(-1)·F(0)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( 1/(n^{p}+k^{p}) )·pk^{p+(-1)} ] ] = ln(2)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ (npk^{p+(-1)}+k^{p})·e^{(k/n)}·(1/n)^{p+1} ] ] = e

Teorema:

int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = p!·( e+(-1) )

Demostración:

int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] e^{x}

Teorema:

int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = p!·( 1+(-1)·(1/e) )

Demostración:

int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] (-1)·e^{(-x)}

Teorema:

int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = p!·( e+(-1) )

Demostración: [ por inducción ]

int[x = 0]-[1][ x^{p+1}·e^{x} ]d[x] = ...

... [ x^{p+1}·e^{x} ]_{x = 1}^{x = 1}+(-1)·(p+1)·int[x = 1]-[0][ x^{p}·e^{x} ]d[x] = ...

... [ x^{p+1}·e^{x} ]_{x = 1}^{x = 1}+(p+1)·int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = ...

... (-1)·(p+1)·p!·int[x = 1]-[0][ e^{x} ]d[x] = (-1)·(p+1)!·int[x = 1]-[0][ e^{x} ]d[x] = (p+1)!·( e+(-1) )

Teorema:

int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = p!·( 1+(-1)·(1/e) )

Demostración: [ por inducción ]

int[x = 0]-[1][ x^{p+1}·e^{(-x)} ]d[x] = ...

... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(p+1)·int[x = 1]-[0][ x^{p}·e^{(-x)} ]d[x] = ...

... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = ...

... (-1)·(p+1)·p!·int[x = 1]-[0][ e^{(-x)} ]d[x] = ...

... (-1)·(p+1)!·int[x = 1]-[0][ e^{(-x)} ]d[x] = (p+1)!·( 1+(-1)·(1/e) )

Teorema:

int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = p!

Demostración:

int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] e^{x}

Teorema:

int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = p!

Demostración:

int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] (-1)·e^{(-x)}

Teorema:

int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = p!

Demostración: [ por inducción ]

int[x = (-oo)]-[0][ x^{p+1}·e^{x} ]d[x] = ...

... [ x^{p+1}·e^{x} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[(-oo)][ x^{p}·e^{x} ]d[x] = ...

... [ x^{p+1}·e^{x} ]_{x = 0}^{x = 0}+(p+1)·int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = ...

... (-1)·(p+1)·p!·int[x = 0]-[(-oo)][ e^{x} ]d[x] = (-1)·(p+1)!·int[x = 0]-[(-oo)][ e^{x} ]d[x] = (p+1)!

Teorema:

int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = p!

Demostración: [ por inducción ]

int[x = 0]-[oo][ x^{p+1}·e^{(-x)} ]d[x] = ...

... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(p+1)·int[x = oo]-[0][ x^{p}·e^{(-x)} ]d[x] = ...

... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = ...

... (-1)·(p+1)·p!·int[x = oo]-[0][ e^{(-x)} ]d[x] = (-1)·(p+1)!·int[x = oo]-[0][ e^{(-x)} ]d[x] = (p+1)!

Teorema: [ de Hôpital-Garriga ]

Si f(x) = 1 ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( 1+(-1) ) = (0/0) = 1 = f(x)

Teorema: [ de Hôpital-Garriga ]

Si f(x) = (-1) ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( 1+(-1) ) = ((-0)/0) = (-1) = f(x)

Teorema: [ de Hôpital-Garriga ]

Si f(x) = 0^{n} ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( 0^{n}+(-1)·0^{n} ) = (1/0)·0^{n+1} = 0^{n} = f(x)

Teorema: [ de Hôpital-Garriga ]

Si f(x) = oo^{n} ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

d_{x}[f(x)] = (1/h)·( f(x+h)+(-1)·f(x) ) = (1/h)·( oo^{n}+(-1)·oo^{n} ) = ...

... (1/0)·oo^{n+(-1)} = oo^{n} = f(x)

Ley: [ de ejemplo de teoría ]

Si d_{V}[P_{0}]·V^{2}+PV+(-1)·d_{P}[k]·TP = 0 ==>

V_{min} = (-1)·(1/2)·( 1/d_{V}[P_{0}] )·P

(1/4)·( 1/d_{V}[P_{0}] )·P^{2}+d_{P}[k]·TP = 0

P_{min} = (-1)·2·d_{P}[k]·T·d_{V}[P_{0}]

(PV)_{min} = d_{P}[k]·TP

d_{P}[T(P)]·p = qR <==> p = qR·( 1/(PV)_{min} )·d_{P}[k]·(-1)·P^{2}

Deducción:

d_{V}[ d_{V}[P_{0}]·V^{2}+PV+(-1)·d_{P}[k]·TP ] = ...

... d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV]+d_{V}[ (-1)·d_{P}[k]·TP ] = ...

... d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV]+0 = d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV] = ...

... d_{V}[P_{0}]·d_{V}[V^{2}]+P·d_{V}[V] = d_{V}[P_{0}]·2V+P

d_{V}[P_{0}]·2V+P = 0

d_{V}[P_{0}]·2V = d_{V}[P_{0}]·2V+0 = d_{V}[P_{0}]·2V+(P+(-P)) = ...

... ( d_{V}[P_{0}]·2V+P )+(-P) = 0+(-P) = (-P)·

V = ( (1/2)·(1/d_{V}[P_{0}])·(d_{V}[P_{0}]·2) )·V = ...

... (1/2)·(1/d_{V}[P_{0}])·( (d_{V}[P_{0}]·2)·V ) = (-1)·(1/2)·(1/d_{V}[P_{0}])·P

d_{P}[T(P)] = (PV)_{min}·(1/d_{P}[k])·(-1)·(1/P)^{2}

Ley:

Si ( P+d_{xyz}^{3}[q(x,y,z)]·gh )·V = kT ==>

q(x,y,z) = kT·(1/(gh))·(1/V)·xyz+(-1)·P·(1/(gh))·xyz

Ley:

Si ( P+d_{xy}^{2}[q(x,y)]·g )·V = kT ==>

q(x,y) = kT·(1/g)·(1/V)·xy+(-1)·P·(1/g)·xy

Ley:

Si ( P+d_{xy}^{2}[q(x,y)]·g )·V = kT·xya^{2} ==>

q(x,y) = kT·(1/g)·(1/V)·(1/4)·(axy)^{2}+(-1)·P·(1/g)·xy

Ley:

Si ( P+d_{x}[m(x)]·u^{2} )·V = kT ==>

m(x) = kT·(1/u)^{2}·(1/V)·x+(-1)·P·(1/u)^{2}·x

Rezo al Mal:

Los hombres no tienen motor de curvatura,

y no pueden ir a ver a su mujer,

pero no son maricones.

Los extraterrestres tienen motor de curvatura,

y pueden ir a ver a su mujer,

pero son maricones.

Definición:

er-h[p](x) = sum[k = 0]-[oo][ (1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ]

er-h[p](x) = sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·x^{k} ] = ...

... (1/(p+1))·x^{p+1} [o(x)o] e^{x}

er-h[p](-x) = sum[k = 0]-[oo][ (-1)^{k}·(1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ]

er-h[p](-x) = sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (-1)^{k}·(1/k!)·x^{k} ] = ...

... sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·(-x)^{k} ] = (1/(p+1))·x^{p+1} [o(x)o] e^{(-x)}

Teorema:

int[ x^{p}·e^{x} ]d[x] = er-h[p](x)

int[ x^{p}·e^{(-x)} ]d[x] = (-1)·er-h[p](-x)

Teorema:

er-h[p](1) = p!·e

er-h[p](0) = p!

er-h[p](-1) = p!·(1/e)

Demostración:

er-h[p](x) = sum[j = 0]-[oo][ (1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ] = ...

... sum[j = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·x^{k} ] = p!·sum[j = 0]-[oo][ (1/k!)·x^{k} ]

Teorema:

d_{x}[er-h[p](-x)] = (-1)·x^{p}·e^{(-x)}

Demostración:

j = k+(-1)

d_{x}[er-h[p](-x)] = sum[k = 0]-[oo][ (-1)^{k}·(1/(k+(-1))!)·x^{(k+(-1))+p} ] = ...

... sum[k = 0]-[oo][ (-1)^{j+1}·(1/j!)·x^{j+p} ] = ...

... (-1)·x^{p}·sum[k = 0]-[oo][ (-1)^{j}·(1/j!)·x^{j} ] = ...

... (-1)·x^{p}·sum[k = 0]-[oo][ (1/j!)·(-x)^{j} ] = (-1)·x^{p}·e^{x}

Principio:

El que es,

es.

El que no es,

no es.

Ley:

Afirmación Verdadera:

El fiel es,

y el infiel no es.

Negación Falsa:

El fiel no es,

y el infiel es.

Ley:

Afirmación Verdadera:

No es ninguien,

no siendo los infieles,

estando todo fiel muerto.

Negación Falsa:

Es toto-hoimbre,

siendo los fieles,

estando todo-algún fiel vivo.

Anexo

Esta falsedad no es de Cygnus-Kepler,

porque hay fieles ascendidos,

y no lo puede decir el Mal.

Rezo al Mal desde Cygnus-Kepler:

Yo que soy hombre,

no soy,

amando al próximo,

no como a mi mismo.

Él que es extraterrestre,

es,

amando al prójimo,

como a mi mismo.

Teorema:

p^{m} =[m]= p

Demostración: [ por inducción ]

(p+1)^{m} = p^{m}+mk+1 =[m]= p^{m}+1 =[m]= p+1

Teorema:

p^{m} =[m]= mp

Demostración: [ por inducción ]

(p+1)^{m} = p^{m}+mk+1 =[m]= p^{m}+1 =[m]= mp+1

Definición:

f(a) = b <==> a =[m]= b

Teorema:

f(1) = 1

Demostración:

1 =[m]= 1

Teorema:

f(a+b) = f(a)+f(b)

Demostración:

a+b =[m]= a+b

f(a+b) = a+b

a =[m]= a & b =[m]= b

f(a+b) = a+b = f(a)+f(b)

Teorema:

f(ab) = f(a)·f(b)

Demostración:

ab =[m]= ab

f(ab) = ab

a =[m]= a & b =[m]= b

f(ab) = ab = f(a)·f(b)

Teorema:

Si a =[m]= 1 ==> sum[r = 0]-[m+(-1)][ f(a) ] = m+(-1)

Demostración:

a =[m]= 1

f(a) = 1

Teorema:

Si a =[m]= p^{m+(-1)} ==> sum[r = 0]-[m+(-1)][ f(a) ] = m+(-1)

Demostración:

a =[m]= p^{m+(-1)} =[m]= 1

f(a) = 1

Teorema:

Si a =[2]= 0 ==>

x^{2}+ax =[2]= p <==> x =[2]= p

Demostración:

a =[2]= 0

f(a) = 0

x+ax =[2]= x^{2}+ax =[2]= p

f(x) = f(x)+f(a)·f(x) = f(x)+f(ax) = f(x+ax) = p

x =[2]= p

Teorema:

Si a =[2]= 1 ==>

x^{2}+ax =[2]= p <==> x =[2]= p

Demostración:

a =[2]= 1

f(a) = 1

ax =[2]= 2x+ax =[2]= x^{2}+ax =[2]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[2]= p

Definición: [ de función de Euler ]

H(ab) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·b·Prod[q | b][ (2+(-1)·(1/q)) ]

Teorema:

H(1) = 1

Demostración:

H(1) = H(1·1) = 1·Prod[p | 1][ ( 2+(-1)·(1/p) ) ]·1·Prod[q | 1][ (2+(-1)·(1/q)) ] = 1

Teorema:

H(a) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]

Demostración:

H(a) = H(a·1) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·1·Prod[q | 1][ (2+(-1)·(1/q)) ] = ...

... a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·1

Teorema:

H(ab) = H(a)·H(b)

Demostración:

H(a·b) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·b·Prod[q | b][ (2+(-1)·(1/q)) ] = H(a)·H(b)

Teorema:

H(p^{m}) = 2p^{m}+(-1)·p^{m+(-1)}

Teorema:

H(p) = 2p+(-1)

Teorema:

Sea p =[m]= n ==>

p^{m} =[m]= 2n+(-1) <==> p =[m]= n =[m]= 1

Demostración:

p^{m}·(2p+(-1)) =[m]= (2n+(-1))·(2p+(-1))

H(p^{m+1}) =[m]= H(n)·H(p) = H(np)

p^{m+1} =[m]= np

p^{m} =[m]= n

2n+(-1) =[m]= p^{m} =[m]= n

n =[m]= 1

p =[m]= n =[m]= 1

Teorema:

3^{2} =[2]= 5 <==> 3 =[2]= 1

Demostración:

9+(-5) = 4 = 2·2 

3+(-1) = 2

Teorema:

4^{3} =[3]= 7 <==> 4 =[3]= 1

Demostración:

64+(-7) = 57 = 3·19

4+(-1) = 3

Teorema:

5^{4} =[4]= 9 <==> 5 =[4]= 1

Demostración:

625+(-9) = 616 = 4·154

5+(-1) = 4

Teorema:

8^{7} =[7]= 15 <==> 8 =[7]= 1

Demostración:

2,097,152+(-15) = 2,097,137 = 7·299,591

8+(-1) = 7

Teorema:

9^{8} =[8]= 17 <==> 9 =[8]= 1

Demostración:

43,046,721+(-17) = 43,046,704 = 8·5,380,838

9+(-1) = 8

Teorema:

x^{2} =[2]= a <==> x =[2]= a

Demostración:

Sea x = y+a ==>

(y+a)^{2} = y^{2}+2ya+a^{2} =[2]= y+a 

y+a =[2]= a

x+(-a) = y =[2]= 0

Teorema:

x^{2} =[2]= 2k <==> x =[2]= 2k

Demostración:

4k^{2}+(-2)·k = 2·( 2k^{2}+(-k) )

Teorema:

x^{2} =[2]= 2k+1 <==> x =[2]= 2k+1

Demostración:

4k^{2}+4k+1+(-2)·k+(-1) = 2·( 2k^{2}+k )

Teorema:

x^{3} =[3]= a <==> x =[3]= a

Demostración:

Sea x = y+a ==>

(y+a)^{3} = y^{3}+3y^{2}a+3ya^{2}+a^{3} =[3]= y+a 

y+a =[3]= a

x+(-a) = y =[3]= 0

Teorema:

x^{3} =[3]= 3k <==> x =[3]= 3k

Demostración:

27k^{3}+(-3)·k = 3·( 9k^{3}+(-k) )

Teorema:

x^{3} =[3]= 3k+1 <==> x =[3]= 3k+1

Demostración:

27k^{3}+27k^{2}+9k+1+(-3)·k+(-1) = 3·( 9k^{3}+9k^{2}+2k )

Teorema:

x^{3} =[3]= 3k+2 <==> x =[3]= 3k+2

Demostración:

27k^{3}+54k^{2}+36k+8+(-3)·k+(-2) = 3·( 9k^{3}+18k^{2}+11k+2 )

Teorema:

a^{2} =[4]= 2a

Demostración: 

a = 2k 

Teorema:

a =[4]= 1

Demostración:

a = 4k+1

Teorema:

x^{4} =[4]= a <==> ( 2x =[4]= a || 2x+1 =[4]= 3a )

Demostración:

Sea x = y+a ==>

(y+a)^{4} = y^{4}+4y^{3}a+6·(ya)^{2}+4ya^{3}+a^{4} =[4]= ( y^{2}+a^{2} )^{2} =[4]= ...

...  2y^{2}+2a^{2} =[4]= 2y+2a 

2y+2a =[4]= a

2x+(-a) = 2y+a =[4]= 0

2y^{2}+2a^{2} =[4]= 2y+1 =[4]= a

2x+1 =[4]= 3a

Teorema:

x^{4} =[4]= 4k <==> x =[4]= 2k

Demostración:

16k^{4}+(-4)·k = 4·( 4k^{4}+(-k) )

Teorema:

x^{4} =[4]= 4k+1 <==> x =[4]= 2k+1 =[4]= 6k+1

Demostración:

1,296k^{4}+864k^{3}+216k^{2}+24k+1+(-4)·k+-1 = 4·( 324k^{4}+216k^{2}+54k^{2}+5k )

electro-magnetismo y mecánica-ingeniería y ecuaciones-en-derivadas-parciales y mecánica-física y análisis-matemático-6 y medicina

Examen de electro-magnetismo:

Principio:

E(x,y,z) = qk·(1/r)^{3}·a·< x^{2},y^{2},z^{2} >

E(yz,zx,xy) = qk·(1/r)^{4}·a^{2}·< (yz)^{2},(zx)^{2},(xy)^{2} >

Ley:

div[ E(x,y,z) ] = ?

Anti-div[ E(yz,zx,xy) ] = ?

Ley:

Anti-Potencial[ E(x,y,z) ] = ?

Potencial[ E(yz,zx,xy) ] = ?

Ley: [ de corrección del examen ]

div[ E(x,y,z) ] = d_{x(yz)}^{2}[ Anti-Potencial[ E(x,y,z) ] ]

Anti-div[ E(yz,zx,xy) ] = d_{x(yz)}^{2}[ Potencial[ E(yz,zx,xy) ] ]

Ley:

R·d_{t}[q(t)]+(-C)·p(t) = W·f(ut)·e^{ut}

p(t) = W·( 1/(uR·d_{ut}[f(ut)]+(-C)·f(ut)) )·f(ut)·e^{ut}

q(t) = W·( ut /o(ut)o/ (uR·f(ut)+(-C)·int[ f(ut) ]d[ut]) ) [o(ut)o] f(ut) [o(ut)o] e^{ut}

Ley:

R·d_{t}[q(t)]+C·p(t) = W·f(ut)·e^{(-1)·ut}

p(t) = W·( 1/((-u)·R·d_{ut}[f(ut)]+C·f(ut)) )·f(ut)·e^{(-1)·ut}

q(t) = W·( ut /o(ut)o/ ((-u)·R·f(ut)+C·int[ f(ut) ]d[ut]) ) [o(ut)o] f(ut) [o(ut)o] e^{(-1)·ut}

Ley:

Sea ( d_{t}[ I_{cx} ] = 0 & d_{t}[ I_{cy} ] = 0 ) ==>

Si d[M_{1}(t)] = (1/2)·mgx·(1/s)^{2}·cos(nw)·d[w] ==>

M_{1}(t) = (1/2)·mg·(x/n)·(1/s)^{2}·sin(nw)

Si d[ d[M_{2}(t)] ] = mg·(1/s)^{2}·sin(nw)·cos(nw)·d[y]d[w] ==>

M_{2}(t) = mg·(y/n)·(1/s)^{2}·(1/2)·( sin(nw) )^{2}

M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( I_{cx}/I_{cy} ) & I_{cx} [< I_{cy} )

Ley:

Sea d_{t}[ I_{c} ] = 0 ==>

Si d[M_{1}(t)] = (1/2)·I_{c}·u^{2}·cos(nw)·d[w] ==>

M_{1}(t) = (1/2)·I_{c}·u^{2}·(1/n)·sin(nw)

Si d[ d[M_{2}(t)] ] = I_{c}·u^{2}·(1/x)·sin(nw)·cos(nw)·d[x]d[w] ==>

M_{2}(t) = I_{c}·u^{2}·ln(ax)·(1/n)·(1/2)·( sin(nw) )^{2}

M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( ( 1/ln( aI_{c}·(1/(md)) ) ) ) & aI_{c} >] md·e )

Ley: [ del calor electro-magnético ]

div[ E_{e}(x,y,t) ] = (-2)·(1/c)·B_{e}(x,y,t)

Deducción:

E_{e}(x,y,t)+int[ B_{e}(x,y,t) ]d[t] = 0 = m·d_{tt}^{2}[ < x,y > ]

x(t) = ct·( cos(w) )^{2}

y(t) = ct·( sin(w) )^{2}

div[ E_{e}(x,y,t) ]+div[ inr[ B_{e}(x,y,t) ]d[t] ] = 0^{2}

div[ int[ B_{e}(x,y,t) ]d[t] ] = ( 1/(d[x]+d[y]) )·(d[x]+d[y]) [o] div[ int[ B_{e}(x,y,t) ]d[t] ]

div[ E_{e}(x,y,t) ]+2·(1/c)·B_{e}(x,y,t) = 0^{2}

div[ E_{e}(x,y,t) ] = (-2)·(1/c)·B_{e}(x,y,t)

Ley: [ del calor gravito-magnético ]

div[ E_{g}(x,y,t) ] = (-2)·(1/c)·B_{g}(x,y,t)

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

u(x,y,(1/u)) = K(ax,ay)

u(x,y,t) = ( (1+(-1)·ut)·H(ax,ay)+ut·K(ax,ay) || 1 )·e^{ax+ay+(-1)·act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

u(x,y,(1/u)) = K(ax,ay)

u(x,y,t) = ( (1+(-1)·ut)·H(ax,ay)+ut·K(ax,ay) || 1 )·e^{ax+ay+act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(0,0,t) = f(ut)

u(p,q,t) = g(ut)

u(x,y,t) = ...

... ( (1/2)·( (1+(-1)·(x/p))·f(ut)+(1+(-1)·(y/q))·f(ut) )+(1/2)·( (x/p)·g(ut)+(y/q)·g(ut) ) || 1 )·...

... e^{ax+ay+(-1)·act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(0,0,t) = f(ut)

u(p,q,t) = g(ut)

u(x,y,t) = ...

... ( (1/2)·( (1+(-1)·(x/p))·f(ut)+(1+(-1)·(y/q))·f(ut) )+(1/2)·( (x/p)·g(ut)+(y/q)·g(ut) ) || 1 )·...

... e^{ax+ay+act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(0,q,t) = f(ut)

u(p,0,t) = g(ut)

u(x,y,t) = ?

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(0,q,t) = f(ut)

u(p,0,t) = g(ut)

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ...

... (1/2)·( e^{ax+ay+ac·it || ln( H(ax,ay) )+act}+e^{ax+ay+ac·it || ln( H(ax,ay) )+(-1)·act} )

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ...

... (1/2)·( e^{ax+ay+act || ln( H(ax,ay) )+act}+e^{ax+ay+act || ln( H(ax,ay) )+(-1)·act} )

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(0,y,0) = F(ay)

u(r,y,0) = G(ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(0,y,0) = F(ay)

u(r,y,0) = G(ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(x,y,0)] = h(ax,ay)

u(x,y,t) = (1/2)·sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·act·0 || (4t)^{(1/2)}]-[h(ax,ay)+act·0 || (4t)^{(1/2)}][ w ]d[w] ]·e^{ax+ay+ac·it || 0}

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(x,y,0)] = h(ax,ay)

u(x,y,t) = (1/2)·sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·act·0 || (4t)^{(1/2)}]-[h(ax,ay)+act·0 || (4t)^{(1/2)}][ w ]d[w] ]·e^{ax+ay+act || 0}

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(0,y,0)] = ac·f(ay)

d_{t}[u(r,y,0)] = ac·g(ay)

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(0,y,0)] = ac·f(ay)

d_{t}[u(r,y,0)] = ac·g(ay)

u(x,y,t) = ?

Motores a combustión de explosión acotada:

Ley:

Sea d[I_{c}] = (1/s)^{2}·Mrv·d[t] ==>

Si (I_{c}/2)·d_{t}[w]^{2} = qgh·cos(ut) ==>

x(t) = (M/(md))·(1/s)^{2}·rvt

w(t) = (1/u)·( 2qgh·(1/(Mrv))·us^{2}·( ln(ut) [o(ut)o] sin(ut) ) )^{[o(ut)o] (1/2)}

(1/u) [< t [< (pi/u)

Ley:

Sea d[I_{c}] = (1/s)^{2}·Mrgt·d[t] ==>

Si (I_{c}/2)·d_{t}[w]^{2} = qgh·sin(ut) ==>

x(t) = (M/(md))·(1/s)^{2}·rg·(1/2)·t^{2}

w(t) = (1/u)·( 4qgh·(1/(Mrg))·(us)^{2}·( (1/(ut)) [o(ut)o] cos(ut) ) )^{[o(ut)o] (1/2)}

(1/u) [< t [< (pi/(2u))

Teorema:

( cos(w) )^{4}+(-1)·( sin(w) )^{4}+i·sin(2w) = e^{2iw}

Teorema:

( cos(w) )^{4}+( sin(w) )^{4}+(1/2)·( sin(2w) )^{2} = 1

Ley:

Sea ( d_{t}[ I_{cx} ] = 0 & d_{t}[ I_{cy} ] = 0 ) ==>

Si d[ d[M(t)] ] = qg·(1/s)^{2}·sin(nw)·cos(nw)·d[x]d[w] ==>

M(t) = qg·(x/n)·(1/s)^{2}·(1/2)·( sin(nw) )^{2}

(I_{c}/2)·d_{t}[w]^{2} = qgx·(1/(ns))^{2}·(1/4)·( nw+(-1)·(1/2)·sin(2nw) )

x(t) = I_{c}·(1/(md))

w(t) = (1/n)·Anti-[ ( s /o(s)o/ ( (1/4)·s^{2}+(1/8)·cos(2s) ) )^{[o(s)o](1/2)}]-( ...

... ( (1/(md))·qg )^{(1/2)}·(1/s)·t )

Ley:

Sea d_{t}[ I_{c} ] = 0 ==>

Si d[ d[M(t)] ] = I_{c}·u^{2}·(1/x)·sin(nw)·cos(nw)·d[x]d[w] ==>

M(t) = I_{c}·u^{2}·ln(ax)·(1/n)·(1/2)·( sin(nw) )^{2}

(I_{c}/2)·d_{t}[w]^{2} = I_{c}·u^{2}·ln(ax)·(1/n)^{2}·(1/4)·( nw+(-1)·(1/2)·sin(2nw) )

x(t) = I_{c}·(1/(md))

w(t) = (1/n)·Anti-[ ( s /o(s)o/ ( (1/4)·s^{2}+(1/8)·cos(2s) ) )^{[o(s)o](1/2)}]-( ...

... ( ln( aI_{c}·(1/md) ) )^{(1/2)}·ut )

Ecuaciones de densidades:

Leyes de agua y aceite:

Ley: 

d_{x}[u(x,y)]+d_{y}[u(x,y)] = (m/V)·xy

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·( (m/(4V))·yx^{2} || (m/(4V))·xy^{2} || m )

Ley:

d_{x}[u(x,y)]+d_{y}[u(x,y)] = (-V)·m·( 1/(xy) )^{2}

u(x,0) = m·F(ax)

u(x,r) = m·G(ax)

u(x,y) = ( (1+(-1)·(y/r))·F(ax)+(y/r)·G(ax) || 1 )·( (V/2)·( m/(xy^{2}) ) || (V/2)·( m/(yx^{2}) ) || m )

Ley: [ de ola de mar ]

d_{x}[u(x,y)]+d_{y}[u(x,y)] = m·(1/a)·(1/(xy))

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·( (1/2)·(m/(ay))·ln(ax) || (1/2)·(m/(ax))·ln(ay) || m )

Ley: 

d_{x}[u(x,y)]+d_{y}[u(x,y)]+a·u(x,y) = (m/V)·xy

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·....

... ( (m/(6V))·yx^{2} || (m/(6V))·xy^{2} || (1/(3V))·(m/a)·xy || m )

Ley:

d_{x}[u(x,y)]+d_{y}[u(x,y)]+a·u(x,y) = (-V)·m·( 1/(xy) )^{2}

u(x,0) = m·F(ax)

u(x,r) = m·G(ax)

u(x,y) = ( (1+(-1)·(y/r))·F(ax)+(y/r)·G(ax) || 1 )·...

... ( (V/3)·( m/(xy^{2}) ) || (V/3)·( m/(yx^{2}) ) || (-1)·(V/3)·(m/a)·( 1/(xy) )^{2} || m )

Arte:

Sea u(x) = e^{(-x)} ==>

[Ax][ f(a)·(1/u)^{0} = f(a) ]

[Ex][ (-1)^{k}·(k+(-1))!·d_{a...a}^{k}[f(a)]·(1/u)^{k} = d_{a...a}^{k}[f(a)] ]

Exposición:

x = (-1)·(1/k)·ln( (-1)^{k}·(k+(-1))! )

Sea z(x) = e^{(-x)}+a ==>

Sea u(x) = e^{(-x)} ==>

d[u] = d[z]

s(u) = 1

d[u] = d[s(u)] = d[1] ==>

Caso 1:

int[x = 0]-[1][ f(a)/(a+(-z)) ]d[z] = int-int[ (-1)·d_{a}[f(a)]·(1/u) ]d[u]d[a] = f(a)

int[ (-1)·d_{a}[f(a)]·(1/u) ]d[u] = d_{a}[f(a)]

(-1)·d_{a}[f(a)]·(1/z) = d_{a}[f(a)]

Caso 2:

int-int[x = 0]-[1][ f(a)/(a+(-z))^{2} ]d[z]d[z] = ...

... int-int-int-int[ d_{aa}^{2}[f(a)]·(1/u)^{2} ]d[u]d[u]d[a]d[a] = f(a)

int-int[ d_{aa}^{2}[f(a)]·(1/u)^{2} ]d[u]d[u] = d_{aa}^{2}[f(a)]

d_{aa}^{2}[f(a)]·(1/z)^{2} = d_{aa}^{2}[f(a)]

Caso 3:

int-int-int[x = 0]-[1][ 2·f(a)/(a+(-z))^{3} ]d[z]d[z]d[z] = ...

... int-int-int-int-int-int[ (-1)·2·d_{aaa}^{2}[f(a)]·(1/u)^{3} ]d[u]d[u]d[u]d[a]d[a]d[a] = f(a)

int-int-int[ (-1)·2·d_{aaa}^{3}[f(a)]·(1/u)^{3} ]d[u]d[u]d[u] = d_{aaa}^{3}[f(a)]

(-1)·2·d_{aaa}^{3}[f(a)]·(1/u)^{3} = d_{aaa}^{3}[f(a)]

Artes: [ de series de Laurent ]

Sea z(x) = e^{(-x)} ==>

Exposición:

x = 0

Arte:

[Ex][ e^{x} = 1+sum[k = 1]-[oo][ (-1)^{k}·(1/k)·( xe^{x} )^{k} ] ]

[Ex][ e^{(-x)} = 1+sum[k = 1]-[oo][ (1/k)·( xe^{(-x)} )^{k} ] ]

Arte:

[Ex][ ( 1/(1+(-x)) ) = 1+sum[k = 1]-[oo][ k!·(1/k)·( xe^{(-x)} )^{k} ] ]

[Ex][ (-1)·( 1/(1+(-x))^{2} ) = (-1)+sum[k = 1]-[oo][ (-1)^{k+1}·(k+1)!·(1/k)·( xe^{(-x)} )^{k} ] ]

Arte:

[Ex][ e-pos[m](x) = m+sum[k = 1]-[oo][ (-1)^{k}·( 1+m·(1/k) )·( xe^{x} )^{k} ] ]

[Ex][ e-neg[m](x) = (-m)+sum[k = 1]-[oo][ (-1)^{k}·( 1+(-m)·(1/k) )·( xe^{x} )^{k} ] ]

Arte:

[Ex][ octopus(x) = 1+sum[k = 1]-[oo][ (-1)^{k}·(k+1)!·(1/k)·( xe^{x} )^{k} ] ]

[Ex][ d_{x}[ octopus(x) ] = 2+sum[k = 1]-[oo][ (-1)^{k}·(k+2)!·(1/k)·( xe^{x} )^{k} ] ]

Arte:

[Ex][ ln(1+x) = (-x)·e^{x}+sum[k = 2]-[oo][ (-1)·k!·(1/k)^{2}·( xe^{x} )^{k} ] ]

[Ex][ ln(1+(-x)) = xe^{(-x)}+sum[k = 2]-[oo][ (-1)^{k+1}·k!·(1/k)^{2}·( xe^{(-x)} )^{k} ] ]

(-0) = 0 = ln(1+0) = ln(1)

Enfermedad de centro de dos mandamientos duales a densidad de carga constante:

Ley:

d_{x}[f(x)] = qaie^{axi}

d_{x}[g(x)] = (-1)·qaie^{(-1)·ayi}

s(y) = x

Robar la intimidad,

sin conexión de luz eléctrica:

No puede duchar-se con cortina opaca.

Ley:

d_{x}[f(x)] = iqa·cos(ax)

d_{x}[g(x)] = (-1)·qa·sin(ax)

f(x)+g(x) = qe^{axi}

Robar la libertad,

sin conexión de luz eléctrica:

No puede salir lloviendo o nublado.

Ley:

d_{x}[f(x)] = (-i)·qa·cos(ax)

d_{x}[g(x)] = (-1)·qa·sin(ax)

f(x)+g(x) = qe^{(-1)·axi}

Terapia con constructor:

Ley:

d_{x}[f(x)] = qae^{ax}

d_{x}[g(x)] = (-1)·qae^{(-1)·ay}

s(y) = x

No robar la intimidad,

con visita de algoritmo interno:

Ley:

d_{x}[f(x)] = qa·cosh(ax)

d_{x}[g(x)] = qa·sinh(ax)

f(x)+g(x) = qe^{ax}

No robar la libertad,

con visita de algoritmo externo:

Ley:

d_{x}[f(x)] = (-1)·qa·cosh(ax)

d_{x}[g(x)] = qa·sinh(ax)

f(x)+g(x) = qe^{(-1)·ax}

Enfermedad de centro de dos mandamientos duales a densidad de carga variable:

Ley:

d_{x}[f(x)] = d_{x}[q(x)]·ie^{axi}

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·ie^{(-1)·ayi}

s(y) = x

Deducción:

int[ d_{x}[q(x)] ]d[x] [o(x)o] int[ ie^{axi} ]d[x] = int[ d_{x}[q(x)] ]d[x] [o(ax)o] int[ ie^{axi} ]d[ax]

Ley:

d_{x}[f(x)] = i·d_{x}[q(x)]·cos(ax)

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·sin(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{axi}

Ley:

d_{x}[f(x)] = (-i)·d_{x}[q(x)]·cos(ax)

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·sin(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{(-1)·axi}

Terapia con constructor:

Ley:

d_{x}[f(x)] = d_{x}[q(x)]·e^{ax}

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·e^{(-1)·ay}

s(y) = x

Ley:

d_{x}[f(x)] = d_{x}[q(x)]·cosh(ax)

d_{x}[g(x)] = d_{x}[q(x)]·sinh(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{ax}

Ley:

d_{x}[f(x)] = (-1)·d_{x}[q(x)]·cosh(ax)

d_{x}[g(x)] = d_{x}[q(x)]·sinh(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{(-1)·ax}

Principio: [ de oftalmología de imagen y sonido ]

Vista sana:

d_{x}[q( (pi/(2a)) )]·d_{y}[p( (-1)·(pi/(2a)) )]+d_{x}[p( (pi/a) )]·d_{y}[q( (0/a) )] = pqa^{2}

Oída sana:

d_{x}[q( (pi/(2a))·i )]·d_{y}[p( (-1)·(pi/(2a))·i )]+d_{x}[p( (pi/a)·i )]·d_{y}[q( (0/a)·i )] = pqa^{2}

Principio: [ de definición de lentes ]

Lentes de Miopía:

f(ax) = (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Lentes de Hipermetropía:

g(ay) = ( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

Ley: [ de gafas de miopía ]

q(x) = qe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] sin(ax) [o(ax)o] f(ax)} = qe^{sin(ax)}

p(x) = pe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] cos(ax) [o(ax)o] f(ax)} = pe^{cos(ax)}

Ley: [ de gafas de hipermetropía ]

p(y) = pe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] sin(ay) [o(ay)o] g(ay)} = pe^{sin(ay)}

q(y) = qe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] cos(ay) [o(ay)o] g(ay)} = qe^{cos(ay)}

Ley: [ de sonotone de miopía ]

q(x) = qe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] sinh(ax) [o(ax)o] f(ax)} = qe^{sinh(ax)}

p(x) = pe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] i·cosh(ax) [o(ax)o] f(ax)} = pe^{i·cosh(ax)}

Ley: [ de sonotone de hipermetropía ]

p(y) = pe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] sinh(ay) [o(ay)o] g(ay)} = pe^{sinh(ay)}

q(y) = qe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] i·cosh(ay) [o(ay)o] g(ay)} = qe^{i·cosh(ay)}

Principio: [ de ecuación de la lente ]

Miopía:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = d_{z}[p(z)]+a·(-1)·(1/(ax))^{n}

f(z,x) = p(z)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Hipermetropía:

d_{z}[g(z,y)]+d_{y}[g(z,y)] = d_{z}[q(z)]+a·(1/(ay))^{n}

g(z,y) = q(z)+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

Ley:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = a·( 1+(-1)·(1/(ax))^{n} )

f(z,x) = az+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{z}[g(z,x)]+d_{x}[g(z,x)] = a·( 1+(1/(ax))^{n} )

g(z,x) = az+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

f(z,x)+g(z,x) = n·(n+1) <==> z = (1/(2a))·n·(n+1)

Si n = 2k ==> (1/2)·n·(n+1) € N

Si n = 2k+1 ==> (1/2)·n·(n+1) € N

Deducción:

d_{z}[f(z,x)] = d_{z}[ az+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{z}[ az ]+d_{z}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{z}[az]+0 = d_{z}[az] = a·d_{z}[z] = a

d_{x}[f(z,x)] = d_{x}[ az+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{x}[ az ]+d_{x}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... 0+d_{x}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{x}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... a·d_{ax}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... a·(-1)·d_{ax}[ ( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = a·(-1)·(1/(ax))^{n}

Ley:

d_{z}[f(z,y)]+d_{y}[f(z,y)] = a·( 2+(-1)·(1/(ay))^{n} )

f(z,y) = 2az+(-1)·( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

d_{z}[g(z,y)]+d_{y}[g(z,y)] = a·( 2+(1/(ay))^{n} )

g(z,y) = 2az+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

( f(z,y)+g(z,y) )^{(1/2)} = n·(n+1) <==> z = (1/(4a))·n^{2}·(n^{2}+2n+1)

Si n = 2k ==> (1/4)·n^{2}·(n^{2}+2n+1) € N

Si n = 2k+1 ==> (1/4)·n^{2}·(n^{2}+2n+1) € N

Deducción:

Si n = 2k+1 ==>

(n^{2}+2n+1) = (n+1)^{2} = (2k+2)^{2} = 4k^{2}+4k+4 = 4·(k^{2}+k+1)

Ley:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = a·( (1/(az))+(-1)·(1/(ax))^{n} )

f(z,x) = ln(az)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{z}[g(z,x)]+d_{x}[g(z,x)] = a·( (-1)·( 1/(1+(-1)·(az)) )+(-1)·(1/(ax))^{n} )

g(z,x) = ln(1+(-1)·(az))+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

f(z,x) = g(z,x) <==> z = (1/(2a))

Deducción:

ln(az) = ln(1+(-1)·(az))

az = 1+(-1)·(az)

2az = 1

z = (1/(2a))

Ley:

d_{z}[f(z,y)]+d_{y}[f(z,y)] = a·( (1/2)·(1/(az))+(1/(ay))^{n} )

f(z,y) = (1/2)·ln(az)+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

d_{z}[g(z,y)]+d_{y}[g(z,y)] = a·( (-1)·( 1/((3/4)+(-1)·(az)) )+(1/(ay))^{n} )

g(z,y) = ln((3/4)+(-1)·(az))+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

f(z,y) = g(z,y) <==> ( z = (1/(4a)) con raíz positiva  || z = (9/(4a)) con raíz negativa )

Deducción:

(1/2)·ln(az) = ln((3/4)+(-1)·(az))

(az)^{(1/2)} = (3/4)+(-1)·(az)

az = (9/16)+(-1)·(3/2)·az+(az)^{2}

0 = (9/16)+(-1)·(5/2)·az+(az)^{2}

az = (1/2)·( (5/2)+(-1)·( (25/4)+(-1)·(9/4) )^{(1/2)} ) = (1/2)·( (5/2)+(-2) ) = (1/4)

z = (1/(4a))

az = (1/2)·( (5/2)+( (25/4)+(-1)·(9/4) )^{(1/2)} ) = (1/2)·( (5/2)+2 ) = (9/4)

z = (9/(4a))

Principio: [ de refracción de la lente ]

sin(arw)+(-1)·cos(ars) = sw·(k+(-j))

(-1)·sin(arw)+cos(ars) = sw·(j+(-k))

w = (pi/2) <==> s = 0

w = 0 <==> s = (pi/2)

Ley:

Si k = j ==> sin(arw) = cos(ars)

Si j = k ==> cos(ars) = sin(arw)

Deducción:

sin(arw)+(-1)·cos(ars) = sw·(k+(-j)) = sw·(k+(-k)) = sw·0

sin(arw) = sin(arw)+0 = sin(arw)+( (-1)·cos(ars)+cos(ars) ) = ( sin(arw)+(-1)·cos(ars) )+cos(ars) = ...

... sw·0+cos(ars) = cos(ars)

Ley:

d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( cos(arw)+(-1)·(1/(ax))^{n} )

f(w,x) = sin(arw)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{rs}[g(s,x)]+d_{x}[g(s,x)] = a·( sin(ars)+(1/(ax))^{n} )

g(s,x) = (-1)·cos(ars)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

f(w,x)+g(s,x) = sw·(k+(-j))

Ley:

d_{rw}[f(w,y)]+d_{y}[f(w,y)] = a·( (-1)·cos(arw)+(1/(ay))^{n} )

f(w,y) = (-1)·sin(arw)+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

d_{rs}[g(s,y)]+d_{y}[g(s,y)] = a·( (-1)·sin(ars)+(-1)·(1/(ay))^{n} )

g(s,y) = cos(ars)+(-1)·( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

f(w,y)+g(s,y) = sw·(j+(-k))

Óptica de miopía de imagen:

Sea n la dioptría ==>

d_{x}[q(x)] = (-1)·q(x)·cos(ax)·a·(ax)^{n}

d_{x}[p(x)] = p(x)·sin(ax)·a·(ax)^{n}

Operación Láser de longitud de onda x = rojo 

f(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] sin(ax) }

g(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] cos(ax) }

Óptica de hipermetropía de imagen:

Sea n la dioptría ==>

d_{y}[p(y)] = p(y)·cos(ay)·a·(ay)^{n}

d_{y}[q(y)] = (-1)·q(y)·sin(ay)·a·(ay)^{n}

Operación Láser de longitud de onda y = verde 

f(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1}+ay ) [o(ay)o] sin(ay) }

g(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1}+ay ) [o(ay)o] cos(ay) }

Óptica de miopía de sonido:

Sea n la dioptría ==>

d_{x}[q(x)] = (-1)·q(x)·cosh(ax)·a·(ax)^{n}

d_{x}[p(x)] = (-i)·p(x)·sinh(ax)·a·(ax)^{n}

Operación Láser de longitud de onda x = rojo 

f(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] sinh(ax) }

g(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] i·cosh(ax) }

Óptica de hipermetropía de sonido:

Sea n la dioptría ==>

d_{y}[p(y)] = p(y)·cosh(ay)·a·(ay)^{n}

d_{y}[q(y)] = i·q(y)·sinh(ay)·a·(ay)^{n}

Operación Láser de longitud de onda y = verde 

f(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1}+ay ) [o(ay)o] sinh(ay) }

g(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1+ay ) [o(ay)o] i·cosh(ay) }

Catarata de miopía de imagen:

d_{x}[q(x)] = (-1)·q(x)·cos(ax)·a·(ax)^{10}

d_{x}[p(x)] = p(x)·sin(ax)·a·(ax)^{10}

Operación Láser de longitud de onda x = rojo

f(x) = e^{( (1/11)·(ax)^{11}+ax ) [o(ax)o] sin(ax) }

g(x) = e^{( (1/11)·(ax)^{11}+ax ) [o(ax)o] cos(ax) }

Catarata de hipermetropía de imagen ( ceguera ):

d_{y}[p(y)] = p(y)·cos(ay)·a·(ay)^{10}

d_{y}[q(y)] = (-1)·q(y)·sin(ay)·a·(ay)^{10}

Operación Láser de longitud de onda y = verde 

f(y) = e^{( (-1)·(1/11)·(ay)^{11}+ay ) [o(ay)o] sin(ay) }

g(y) = e^{( (-1)·(1/11)·(ay)^{11}+ay ) [o(ay)o] cos(ay) }

Ley: [ de Grado en Medicina Teoría Homologada ]

Matemáticas 1: Cálculo diferencial.

Química.

Matemáticas 2: Cálculo integral.

Física: Termodinámica y Cabal sanguíneo.

Espectroscopia de fluido corporal.

Teoría genética de infecciones víricas.

Teoría genética de infecciones bacteria-lógicas.

Quimioterapia de desintegración genética.

Óptica de imagen y sonido.

Psico-neurología de negación de voces esquizofrénicas.

Psico-neurología de doble mandamiento dual.

Neurología de resonancia eléctrica.

Neurología de anti-resonancia eléctrica.

Ley:

Un familiar de un matemático o físico tiene convalidada la teoría de medicina,

porque tiene ya la energía para esas o aquellas medicaciones que se derivan de la teoría,

y solo le faltan las asignaturas de practica de atención y cirugía.

Termodinámica de Medicina:

Fiebre y Termómetro:

Ley:

PV = kT

d_{P}[T(P,V)]·p = qR <==> p = ?

d_{V}[T(P,V)]·v = qR <==> v = ?

Ley:

d_{V}[P_{0}]·V^{2}+d_{P}[V_{0}]·P^{2} = kT

d_{P}[T(P,V)]·p = qR <==> p = ?

d_{V}[T(P,V)]·v = qR <==> v = ?

Ley:

d_{V}[P_{0}]·V^{2}+d_{P}[V_{0}]·P^{2} = kT

d_{PP}^{2}[T(P,V)]·p^{2} = qR <==> p = ?

d_{VV}^{2}[T(P,V)]·v^{2} = qR <==> v = ?

Ley:

PV = d_{T}[k]·T^{2}

d_{P}[T(P,V)]·p = qR <==> p = ?

d_{V}[T(P,V)]·v = qR <==> v = ?

Deducción:

d_{P}[T(P,V)] = d_{P}[ ( ( 1/d_{T}[k] )·PV )^{(1/2)} ] = ...

... (1/2)·( ( 1/d_{T}[k] )·PV )^{(-1)·(1/2)}·( V/d_{T}[k] )

física-en-ingeniería y mecánica-de-fluidos y cálculo-integral-geometría y mecánica-en-física

Preliminares:

Principio:

[Ev][ d_{t}[x] = v ]

Ley:

x(t) = vt+h

Deducción:

x(t) = int[ d_{t}[x] ]d[t] = int[ v ]d[t] = v·int[ d[t] ] = vt+h

Principio:

[Eg][ d_{tt}^{2}[x] = g ]

Ley:

Si g = 0 ==> [Ev][ d_{t}[x] = v ]

Ley:

d_{t}[x] = gt+v

x(t) = g·(1/2)·t^{2}+vt+h

Deducción:

d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ g ]d[t] = g·int[ d[t] ] = gt+v

x(t) = int[ d_{t}[x] ]d[t] = int[ gt+v ]d[t]  = int[ gt ]d[t]+int[ v ]d[t] = g·int[ t ]d[t]+v·int[ d[t] ] = ...

... g·(1/2)·t^{2}+vt+h

Ley:

Sea x(t) = ( r^{n}+(vt)^{n} )^{(1/n)} ==>

d_{t}[x] = ( r^{n}+(vt)^{n} )^{(1/n)+(-1)}·(vt)^{n+(-1)}·v

Deducción:

d_{t}[ ( r^{n}+(vt)^{n} )^{(1/n)} ] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·...

... d_{vt}[ r^{n}+(vt)^{n} ]·d_{t}[vt] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·...

... ( d_{vt}[ r^{n} ]+d_{vt}[ (vt)^{n} ] )·d_{t}[vt] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·...

... ( 0+d_{vt}[ (vt)^{n} ] )·d_{t}[vt] = ...

... d_{r^{n}+(vt)^{n}}[ ( r^{n}+(vt)^{n} )^{(1/n)} ]·d_{vt}[ (vt)^{n} ]·d_{t}[vt]

Ley:

Sea d_{t}[x] = ( c^{(1/n)}+(gt)^{(1/n)} )^{n} ==>

x(t) = ( n/(n+1) )·( c^{(1/n)}+(gt)^{(1/n)} )^{n+1} [o(gt)o] ...

... ( 1/(2+(-1)·(1/n)) )·(gt)^{2+(-1)·(1/n)} [o(gt)o] t

Deducción:

g·d_{gt}[ ( ( n/(n+1) )·( c^{(1/n)}+(gt)^{(1/n)} )^{n+1} [o(gt)o] ...

... ( 1/(2+(-1)·(1/n)) )·(gt)^{2+(-1)·(1/n)} ) [o(gt)o] t ] = ...

g·d_{gt}[ ( ( n/(n+1) )·( c^{(1/n)}+(gt)^{(1/n)} )^{n+1} ]·...

... d_{gt}[ ( 1/(2+(-1)·(1/n)) )·(gt)^{2+(-1)·(1/n)} ]·d_{gt}[t] ] = ...

... g·( c^{(1/n)}+(gt)^{(1/n)} )^{n}·d_{gt}[t] = ( c^{(1/n)}+(gt)^{(1/n)} )^{n}

Ley:

Sea y(t,x) = ax^{2} ==>

Si d_{t}[x] = v ==>

d_{tt}^{2}[y(t,x)] = 2av^{2}

d_{t}[y(t,x)] = 2av^{2}·t

y(t,x) = a·(vt)^{2}

Deducción:

d[y(t,x)] = 2ax·d[x]

d_{t}[y(t,x)] = 2ax·d_{t}[x]

d_{tt}^{2}[y(t,x)] = 2a·( d_{t}[x]^{2}+x·d_{tt}^{2}[x] )

x(t) = int[ d_{t}[x] ]d[t] = int[ v ]d[t] = v·int[ d[t] ] = vt 

Ley:

Sea y(t,x) = ax^{2} ==>

Si d_{tt}^{2}[x] = g ==>

d_{tt}^{2}[y(t,x)] = 6ag^{2}·(1/2)·t^{2}

d_{t}[y(t,x)] = 2ag·(1/2)·t^{2}·gt

y(t,x) = a·( g^{2}·(1/4)·t^{4} )

Deducción:

d[y(t,x)] = 2ax·d[x]

d_{t}[y(t,x)] = 2ax·d_{t}[x]

d_{tt}^{2}[y(t,x)] = 2a·( d_{t}[x]^{2}+x·d_{tt}^{2}[x] )

d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ g ]d[t] = g·int[ d[t] ] = gt

x(t) = int[ d_{t}[x] ]d[t] = int[ gt ]d[t] = g·int[ t ]d[t] = g·(1/2)·t^{2}

t = (2x/g)^{(1/2)}

Ley:

Sea 2·( sin(w) )^{2} = ( 1+(-1)·cos(2w) ) ==>

Sea ( d_{t}[x] = v·sin(ut) & d_{t}[y] = v·( 1+(-1)·cos(ut) ) ==>

d_{t}[r] = 2v·sin((ut)/2)

r(0,2pi) = 8v·(1/u)

Ley:

Sea 2·( cos(w) )^{2} = ( 1+cos(2w) ) ==>

Sea ( d_{t}[x] = v·sin(ut) & d_{t}[y] = v·( 1+cos(ut) ) ==>

d_{t}[r] = 2v·cos((ut)/2)

r((-pi),pi) = 8v·(1/u)

Globos y Drones:

Ley:

Sea d_{t}[x] = uy ==>

Si d_{t}[y] = v ==>

x(y) = u·(1/v)·(1/2)·y^{2}

d_{tt}^{2}[x] = uv

Ley:

Sea d_{t}[x] = uy ==>

Si d_{t}[y] = gt ==>

x(y) = ug·(1/6)·( (2/g)·y )^{(3/2)}

d_{tt}^{2}[x] = ugt

---------------------------------------------------

Procedimiento en coordenadas cartesianas:

---------------------------------------------------

Principio: [ de Fuerza ]

[EF_{k}][ m·d_{tt}^{2}[x] = sum[k = 1]-[n][ F_{k} ] ]

Ley: [ de Impulsión ]

[Ep_{k}][ m·d_{t}[x] = sum[k = 1]-[n][ p_{k} ] ]

Deducción:

int[ m·d_{tt}^{2}[x] ]d[t] = m·int[ d_{tt}^{2}[x] ]d[t] = m·d_{t}[x]

int[ sum[k = 1]-[n][ F_{k} ] ]d[t] = sum[k = 1]-[n][ int[ F_{k} ]d[t] ] = sum[k = 1]-[n][ p_{k} ]

Ley: [ de Energía ]

[EU_{k}][ (m/2)·d_{t}[x]^{2} = sum[k = 1]-[n][ U_{k} ] ]

Deducción:

int[ m·d_{tt}^{2}[x] ]d[x] = int[ m·d_{tt}^{2}[x]·d_{t}[x] ]d[t] = (m/2)·d_{t}[x]^{2}

int[ sum[k = 1]-[n][ F_{k} ] ]d[x] = sum[k = 1]-[n][ int[ F_{k} ]d[x] ] = sum[k = 1]-[n][ U_{k} ]

Ley: [ de Potencia ]

[EN_{k}][ (m/u)·d_{t}[x]^{[o(ut)o] 2} = sum[k = 1]-[n][ N_{k} ] ]

Deducción:

int[ m·d_{tt}^{2}[x] ]d[ d_{t}[x] ] = int[ (m/u)·d_{tt}^{2}[x]^{2} ]d[ut] = (m/u)·d_{t}[x]^{[o(ut)o] 2}

int[ sum[k = 1]-[n][ F_{k} ] ]d[ d_{t}[x] ] = sum[k = 1]-[n][ int[ F_{k} ]d[ d_{t}[x] ] ] = ...

... sum[k = 1]-[n][ N_{k} ]

Fuerza constante:

Ley:

Sea F(t) = F ==>

d_{t}[x] = (F/m)·t

x(t) = (F/m)·(1/2)·t^{2}

Deducción:

d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ (F/m) ]d[t] = (F/m)·int[ d[t] ] = (F/m)·t

x(t) = int[ d_{t}[x] ]d[t] = int[ (F/m)·t ]d[t] = (F/m)·int[ t ]d[t] = (F/m)·(1/2)·t^{2}

Ley:

Sea F(t) = F ==>

U(x) = Fx

(m/2)·d_{t}[x]^{2} = U(x)

Deducción:

U(x) = int[ F ]d[x] = F·int[ d[x] ] = Fx

(m/2)·d_{t}[x]^{2} = (m/2)·( (F/m)·t )^{2} = F·( (F/m)·(1/2)·t^{2} ) = Fx = U(x)

Ley:

Sea F(t) = F ==>

N(d_{t}[x]) = F·d_{t}[x]

(m/u)·d_{t}[x]^{[o(ut)o] 2} = N(d_{t}[x])

Deducción:

N(d_{t}[x]) = int[ F ]d[ d_{t}[x] ] = F·int[ d[ d_{t}[x] ] ] = F·d_{t}[x]

(m/u)·d_{t}[x]^{[o(ut)o] 2} = (m/u)·( (F/m)·t )^{[o(ut)o] 2} = int[ (m/u)·(F/m)^{2} ]d[ut] = ...

... F·( (F/m)·t ) = F·d_{t}[x] = N(d_{t}[x])

Fuerza lineal de carga variable:

Ley:

Sea F(t) = Itg ==>

d_{t}[y] = (1/m)·Ig·(1/2)·t^{2}

y(t) = (1/m)·Ig·(1/6)·t^{3}

Deducción:

d_{t}[y] = int[ d_{tt}^{2}[y] ]d[t] = int[ (1/m)·Itg ]d[t] = (1/m)·Ig·int[ t ]dt = (1/m)·Ig·(1/2)·t^{2}

y(t) = int[ d_{t}[y] ]d[t] = int[ (1/m)·Ig·(1/2)·t^{2} ]d[t] = (1/m)·Ig·(1/2)·int[ t^{2} ]d[t] = ...

... (1/m)·Ig·(1/6)·t^{3}

Ley:

Sea F(t) = Itg ==>

U(y) = (1/m)·(Ig)^{2}·(1/8)·t^{4}

(m/2)·d_{t}[y]^{2} = U(y)

Deducción:

U(y) = int[ Itg ]d[y] = int[ Itg d_{t}[y] ]d[t] = int[ (1/m)·( Ig )^{2}·(1/2)·t^{3}· ]d[t] = ...

... (1/m)·( Ig )^{2}·(1/8)·t^{4}

(m/2)·d_{t}[y]^{2} = (m/2)·( ( (1/m)·Ig )·(1/2)·t^{2} )^{2} = (1/m)·( Ig )^{2}·(1/8)·t^{4} = U(y)

Ley:

Sea F(t) = Itg ==>

N(d_{t}[y]) = (1/m)·( Ig )^{2}·(1/3)·t^{3}

(m/u)·d_{t}[y]^{[o(ut)o] 2} = N(d_{t}[y])

Deducción:

N(d_{t}[y]) = int[ Itg ]d[ d_{t}[y] ] = int[ (1/m)·Itg d_{tt}^{2}[y] ]d[t] = ...

... int[ (1/m)·( Itg )^{2} ]d[t] = (1/m)·( Ig )^{2}·(1/3)·t^{3}

(m/u)·d_{t}[y]^{[o(ut)o] 2} = (m/u)·( ( (1/m)·Ig )·(1/2)·t^{2} )^{[o(ut)o] 2} = ...

... int[ (1/m)·( Ig )^{2}·t^{2} ]d[t] = (1/m)·( Ig )^{2}·(1/3)·t^{3} = N(d_{t}[y])

Fuerzas de amortiguación y de resistencia de fluido:

Horizontal:

Ley:

m·d_{tt}^{2}[x] = (-k)·x

x(t) = re^{(k/m)^{(1/2)}·it}

Deducción:

m·d_{tt}^{2}[x] = m·d_{t}[ d_{t}[x] ] = m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ] ] = ...

... m·d_{t}[ r·d_{t}[ e^{(k/m)^{(1/2)}·it} ] ] = m·d_{t}[ re^{(k/m)^{(1/2)}·it}·(k/m)^{(1/2)}·i ] = ...

... mr·(k/m)^{(1/2)}·i·d_{t}[ e^{(k/m)^{(1/2)}·it} ] = ...

... mr·( (k/m)^{(1/2)}·i )^{2} e^{(k/m)^{(1/2)}·it} = ...

... (-k)·re^{(k/m)^{(1/2)}·it} = (-k)·x

Ley

m·d_{tt}^{2}[x] = (-b)·d_{t}[x]

d_{t}[x] = ve^{(-1)·(b/m)·t}

Deducción:

m·d_{tt}^{2}[x] = m·d_{t}[ d_{t}[x] ] = m·d_{t}[ ve^{(-1)·(b/m)·t} ] = ...

... mv·d_{t}[ e^{(-1)·(b/m)·t} ] = mv·e^{(-1)·(b/m)·t}·(-1)·(b/m) = ...

... (-b)·ve^{(-1)·(b/m)·t} = (-b)·d_{t}[x]

Ley:

U(x) = (-k)·(1/2)·x^{2}

(m/2)·d_{t}[x]^{2} = U(x)

Deducción:

U(x) = int[ (-k)·x ]d[x] = (-k)·int[ x ]d[x] = (-k)·(1/2)·x^{2}

(m/2)·d_{t}[x]^{2} = (m/2)·( i·(k/m)^{(1/2)}·re^{(k/m)^{(1/2)}·it} )^{2} = ...

... (-k)·(1/2)·( r^{2}·e^{(k/m)^{(1/2)}·2it} ) = (-k)·(1/2)·x^{2} = U(x)

Ley:

N(d_{t}[x]) = (-b)·(1/2)·d_{t}[x]^{2}

(m/u)·d_{t}[x]^{[o(ut)o] 2} = N(d_{t}[x])

Deducción:

N(d_{t}[x]) = int[ (-b)·d_{t}[x] ]d[ d_{t}[x] ] = ...

... (-b)·int[ d_{t}[x] ]d[ d_{t}[x] ] = (-b)·(1/2)·d_{t}[x]^{2}

(m/u)·d_{t}[x]^{[o(ut)o] 2} = (m/u)·( ve^{(-1)·(b/m)·t} )^{[o(ut)o] 2} = ...

... (m/u)·int[ ( (-1)·(b/m)·v )^{2}·e^{(-2)·(b/m)·t} ]d[ut] = ...

... (-b)·(1/2)·( v^{2}·e^{(-2)·(b/m)·t} ) = (-b)·(1/2)·d_{t}[x]^{2} = N(d_{t}[x])

Fuerzas de amortiguación y de resistencia de fluido:

Vertical:

Ley:

m·d_{tt}^{2}[y] = (-k)·y+qg

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·qg

Deducción:

m·d_{tt}^{2}[y] = m·d_{t}[ d_{t}[y] ] = m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it}+(1/k)·qg ] ] = ...

... m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ]+d_{t}[ (1/k)·qg ] ] = ...

... m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ]+0 ] = m·d_{t}[ d_{t}[ re^{(k/m)^{(1/2)}·it} ] = ...

... m·d_{tt}^{2}[ re^{(k/m)^{(1/2)}·it} ] = (-k)·re^{(k/m)^{(1/2)}·it} = ...

... (-k)·re^{(k/m)^{(1/2)}·it}+(-1)·qg+qg = (-k)·( re^{(k/m)^{(1/2)}·it}+(1/k)·qg )+qg = (-k)·y+qg

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+qg

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·qg

Deducción:

m·d_{tt}^{2}[y] = m·d_{t}[ d_{t}[y] ] = m·d_{t}[ ve^{(-1)·(b/m)·t}+(1/b)·qg ] = ...

... m·( d_{t}[ ve^{(-1)·(b/m)·t} ]+d_{t}[ (1/b)·qg ] ) = ...

... m·( d_{t}[ ve^{(-1)·(b/m)·t} ]+0 ) = m·d_{t}[ ve^{(-1)·(b/m)·t} ] = (-b)·ve^{(-1)·(b/m)·t} = ...

... (-b)·ve^{(-1)·(b/m)·t}+(-1)·qg+qg = (-b)·( ve^{(-1)·(b/m)·t}+(1/b)·qg )+qg = (-b)·d_{t}[y]+qg

Obertura de hombros y caderas robótica:

Por amortiguador de retorno con empuje de obertura de fluido.

Ley:

m·d_{tt}^{2}[y] = (-k)·y+( sin(w)·qg+sin(s)·pg )

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·( sin(w)·qg+sin(s)·pg )

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+( sin(w)·qg+sin(s)·pg )

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·( sin(w)·qg+sin(s)·pg )

Estiramiento de rodillas y codos robótica:

Por amortiguador de retorno con empuje de obertura de fluido.

Ley:

m·d_{tt}^{2}[y] = (-k)·y+( F+(-1)·qg )

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·( F+(-1)·qg )

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+( F+(-1)·qg )

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·( F+(-1)·qg )

Motores robóticos que aumentan la fuerza según la carga:

Ley:

m·d_{tt}^{2}[y] = (-k)·y+( Itg+qg )

y(t) = re^{(k/m)^{(1/2)}·it}+(1/k)·( Itg+qg )

Ley:

m·d_{tt}^{2}[y] = (-b)·d_{t}[y]+( Itg+qg )

d_{t}[y] = ve^{(-1)·(b/m)·t}+(1/b)·( Itg+qg )+(-1)·(1/b)^{2}·Ig

----------------------------------------------

Procedimiento en coordenadas polares:

----------------------------------------------

Principio: [ de Inercia angular ]

[EI_{ck}][ mdx = sum[k = 1]-[n][ I_{ck} ] ]

[ d ] = ( metro / ( radian )^{2} )

Ley: [ de Impulsión angular ]

[EL_{k}][ md·d_{t}[x] = sum[k = 1]-[n][ L_{k} ] ]

Deducción:

d_{t}[ mdx ] = md·d_{t}[x] = md·d_{t}[x]

d_{t}[ sum[k = 1]-[n][ I_{ck} ] ] = sum[k = 1]-[n][ d_{t}[ I_{ck} ] ] = ...

... sum[k = 1]-[n][ L_{k} ]

Ley: [ de Fuerza angular ]

[EH_{k}][ md·d_{tt}^{2}[x] = sum[k = 1]-[n][ H_{k} ] ]

Deducción:

d_{t}[ md·d_{t}[x] ] = md·d_{t}[ d_{t}[x] ] = md·d_{tt}^{2}[x]

d_{t}[ sum[k = 1]-[n][ L_{k} ] ] = sum[k = 1]-[n][ d_{t}[ L_{k} ] ] = ...

... sum[k = 1]-[n][ H_{k} ]

Principio: [ de Energía angular ]

[EU_{k}][ I_{c}·(1/2)·d_{t}[w]^{2} = sum[k = 1]-[n][ U_{k} ] ]

Ley:

Sea U(w) = U ==>

Si I_{c} = M·(r/s)^{2} ==> 

x(t) = (M/m)·(1/d)·(r/s)^{2}

w(t) = ( (2/M)·U )^{(1/2)}·(s/r)·t

Deducción:

mdx = M·(r/s)^{2}

I_{c}·(1/2)·d_{t}[w]^{2} = M·(r/s)^{2}·(1/2)·d_{t}[ ( (2/M)·U )^{(1/2)}·(s/r)·t ]^{2} = ...

... M·(r/s)^{2}·(1/2)·( ( (2/M)·U )^{(1/2)}·(s/r)·d_{t}[ t ] )^{2} = ...

... M·(r/s)^{2}·(1/2)·( ( (2/M)·U )^{(1/2)}·(s/r) )^{2} = U

Principio: [ Fundamental de la dinámica angular ]

[EM_{k}][ d_{w}[ U(w) ] = sum[k = 1]-[n][ M_{k} ] ]

[ M_{k} ] = ( Joule / Radian )

Ley:

L(t)·(1/2)·d_{t}[w]+I_{c}·d_{tt}^{2}[w] = sum[k = 1]-[n][ M_{k} ]

Deducción:

d_{w}[ I_{c}·(1/2)·d_{t}[w]^{2} ] = (1/d_{t}[w])·d_{t}[ I_{c}·(1/2)·d_{t}[w]^{2} ] ...

... (1/d_{t}[w])·( d_{t}[ I_{c} ]·(1/2)·d_{t}[w]^{2}+I_{c}·d_{t}[ (1/2)·d_{t}[w]^{2} ] ) = ...

... L(t)·(1/2)·d_{t}[w]+I_{c}·d_{tt}^{2}[w]

Ley: [ de Momento de Fuerza ]

Si d_{t}[ I_{c} ] = 0 ==> 

[EM_{k}][ I_{c}·d_{tt}^{2}[w] = sum[k = 1]-[n][ M_{k} ] ]

Ley: [ de Momento de Impulsión ]

Si d_{t}[ I_{c} ] = 0 ==>

[EK_{k}][ I_{c}·d_{t}[w] = sum[k = 1]-[n][ K_{k} ] ]

Deducción:

int[ I_{c}·d_{tt}^{2}[w] ]d[t] = I_{c}·int[ d_{tt}^{2}[x] ]d[t] = I_{c}·d_{t}[w]

int[ sum[k = 1]-[n][ M_{k} ] ]d[t] = sum[k = 1]-[n][ int[ M_{k} ]d[t] ] = ...

... sum[k = 1]-[n][ K_{k} ]

Ley: [ de Potencia angular ]

Si d_{t}[ I_{c} ] = 0 ==>

[EN_{k}][ (I_{c}/u)·d_{t}[w]^{[o(ut)o] 2} = sum[k = 1]-[n][ N_{k} ] ]

Deducción:

int[ I_{c}·d_{tt}^{2}[w] ]d[ d_{t}[w] ] = int[ (I_{c}/u)·d_{tt}^{2}[w]^{2} ]d[ut] = ...

.. (I_{c}/u)·d_{t}[w]^{[o(ut)o] 2}

int[ sum[k = 1]-[n][ M_{k} ] ]d[ d_{t}[w] ] = sum[k = 1]-[n][ int[ M_{k} ]d[ d_{t}[w] ] ] = ...

... sum[k = 1]-[n][ N_{k} ]

Ley:

Si ( d_{t}[ I_{c} ] = 0 & M(w) = F·(x/s) ) ==> 

d_{t}[w] = (1/I_{c})·F·(x/s)·t

w(t) = (1/I_{c})·F·(x/s)·(1/2)·t^{2}

Deducción:

Problema.

Ley:

Si ( d_{t}[ I_{c} ] = 0 & M(w) = F·(x/s) ) ==> 

U(w) = F·(x/s)·w

I_{c}·d_{t}[w]^{2} = U(w)

Deducción:

U(w) = int[ M(w) ]d[w] = int[ F·(x/s) ]d[w] = F·(x/s)·int[ d[w] ] = F·(x/s)·w

(I_{c}/2)·d_{t}[w]^{2} = (I_{c}/2)·( (1/I_{c})·F·(x/s)·t )^{2} = ...

... F·(x/s)·( (1/I_{c})·F·(x/s)·(1/2)·t^{2} ) = F·(x/s)·w = U(w)

Ley:

Si ( d_{t}[ I_{c} ] = 0 & M(w) = F·(x/s) ) ==> 

N(d_{t}[w]) = F·(x/s)·d_{t}[w]

(I_{c}/u)·d_{t}[w]^{[o(ut)o] 2} = N(d_{t}[w])

Deducción:

N(d_{t}[w]) = int[ M(w) ]d[ d_{t}[w] ] = int[ F·(x/s)·d_{tt}^{2}[w] ]d[t] = ...

... int[ (1/I_{c})·( F·(x/s) )^{2} ]d[t] = (1/I_{c})·( F·(x/s) )^{2}·int[ d[t] ] = ...

... (1/I_{c})·( F·(x/s) )^{2}·t = F·(x/s)·d_{t}[w]

(I_{c}/u)·d_{t}[w]^{[o(u)o] 2} = (I_{c}/u)·( (1/I_{c})·F·(x/s)·t )^{[o(ut)o] 2} = ...

... (I_{c}/u)·int[ ( (1/I_{c})·F·(x/s) )^{2} ]d[ut] = ...

...(1/I_{c})·( F·(x/s) )^{2}·int[ d[t] ] = (1/I_{c})·( F·(x/s) )^{2}·t = ...

... F·(x/s)·d_{t}[w] = N(d_{t}[w])

Inercias angulares constantes:

Principio:

[Ef][ I_{c} = int[ ( (r·f(n))/s )^{2}·d_{n}[m(n)] ]d[n] ]

Ley:

Si f(n) = n^{0} ==> I_{c} = int[ (r/s)^{2}·d_{n}[m(n)] ]d[n]

Si f(n) = (n/r) ==> I_{c} = int[ (n/s)^{2}·d_{n}[m(n)] ]d[n]

Principio:

[Ef][Eg][ I_{c} = int-int[ (1/2)·( ( (r·f(p))/s )^{2}+( (r·g(q))/s )^{2} )·d_{pq}^{2}[m(p,q)] ]d[p]d[q] ]

Ley:

Si ( f(p) = p^{0} & g(q) = q^{0} ) ==> I_{c} = int-int[ (r/s)^{2}·d_{pq}^{2}[m(p,q)] ]d[p]d[q]

Si ( f(p) = (p/r) & g(q) = (q/r) ) ==> ...

... I_{c} = int-int[ (1/2)·( (p/s)^{2}+(q/s)^{2} )·d_{pq}^{2}[m(p,q)] ]d[p]d[q]

Ley:

Sea ( U(w) = U & F(x) = int[ f(x) ]d[x] ) ==>

Si I_{c} = int[ (r/s)^{2}·Ma·f(an) ]d[n] ==> 

I_{c} = (r/s)^{2}·M·F(an)

x(t) = (1/(md))·(r/s)^{2}·M·F(an)

w(t) = ( 2U )^{(1/2)}·(s/r)·( 1/(M·F(an)) )^{(1/2)}·t

K(t) = ( 2U )^{(1/2)}·(r/s)·( M·F(an) )^{(1/2)}

Ley:

Sea U(w) = U ==>

Si I_{c} = int[ (n/s)^{2}·Ma ]d[n] ==> 

I_{c} = (1/3)·(n/s)^{2}·Man

x(t) = (1/(md))·(1/3)·(n/s)^{2}·Man

w(t) = ( 6U )^{(1/2)}·(s/n)·( 1/(Man) )^{(1/2)}·t

K(t) = ( 6U )^{(1/2)}·(1/3)·(n/s)·( Man )^{(1/2)}

Ley:

Sea ( U(w) = U & F(x) = int[ f(x) ]d[x] & G(x) = int[ g(x) ]d[x] ) ==>

Si I_{c} = int-int[ (r/s)^{2}·Ma^{2}·f(ap)·g(aq) ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·F(ap)·G(aq)

x(t) = (1/(md))·(r/s)^{2}·M·F(ap)·G(aq)

w(t) = ( 2U )^{(1/2)}·(s/r)·( 1/(M·F(ap)·G(aq)) )^{(1/2)}·t

K(t) = ( 2U )^{(1/2)}·(r/s)·( M·F(an)·G(aq) )^{(1/2)}

Deducción:

I_{c} = int-int[ (r/s)^{2}·M·f(ap)·g(aq) ]d[ap]d[aq] = (r/s)^{2}·M·int-int[ f(ap)·g(aq) ]d[ap]d[aq] = ...

... (r/s)^{2}·M·int[ g(aq)·int[ f(ap) ]d[ap] ]d[aq] = (r/s)^{2}·M·int[ g(aq)·F(ap) ]d[aq] = ...

... (r/s)^{2}·M·F(ap)·int[ g(aq) ]d[aq] = (r/s)^{2}·M·F(ap)·G(aq)

Ley:

Sea ( U(w) = U & F(x) = int[ f(x) ]d[x] & G(x) = int[ g(x) ]d[x] ) ==>

Si I_{c} = int-int[ (r/s)^{2}·Ma^{2}·( f(ap)+g(aq) ) ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·( F(ap)·aq+ap·G(aq) )

x(t) = (1/(md))·(r/s)^{2}·M·( F(ap)·aq+ap·G(aq) )

w(t) = ( 2U )^{(1/2)}·(s/r)·( 1/(M·( F(ap)·aq+ap·G(aq) )) )^{(1/2)}·t

K(t) = ( 2U )^{(1/2)}·(r/s)·( M·( F(ap)·aq+ap·G(aq) ) )^{(1/2)}

Ley:

Sea ( U(w) = U & p = r·sin(nw) & q = r·cos(nw) ) ==>

Si I_{c} = int-int[ (1/2)·( (p/s)^{2}+(q/s)^{2} )·Ma^{2} ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·(1/4)·npi·(ar)^{2}

x(t) = (1/(md))·(r/s)^{2}·M·(1/4)·npi·(ar)^{2}

w(t) = ( (8/(npi))·U )^{(1/2)}·(s/r)·(1/(ar))·(1/M)^{(1/2)}·t

K(t) = ( (8/(npi))·U )^{(1/2)}·(r/s)·(ar)·M^{(1/2)}

Deducción:

d[p] = nr·cos(nw)·d[w] & d[q] = nr·(-1)·sin(nw)·d[w]

d[p]d[q] = (nr)^{2}·cos(nw)·(-1)·sin(nw)·d[w]d[w]

Ley:

Sea ( U(w) = U & p = (r/i)·sinh(nw) & q = r·cosh(nw) ) ==>

Si I_{c} = int-int[ (1/2)·( (p/s)^{2}+(q/s)^{2} )·Ma^{2} ]d[p]d[q] ==> 

I_{c} = (r/s)^{2}·M·(1/4)·npi·(ar)^{2}

Motores de rotación.

Ley:

Sea U(w) = U ==>

Si d[I_{c}] = (1/s)^{2}·Mrv·d[t] ==>

x(t) = (1/(md))·(1/s)^{2}·Mrvt

w(t) = ( (8/M)·(1/(rv))·U )^{(1/2)}·st^{(1/2)}

Ley:

Sea U(w) = U ==>

Si d[I_{c}] = (1/s)^{2}·Mrgt·d[t] ==>

x(t) = (1/(md))·(1/s)^{2}·Mrg·(1/2)·t^{2}

w(t) = ( (4/M)·(1/(rg))·U )^{(1/2)}·s·ln(ut)

Articulaciones robóticas y de vehículo.

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mv·d[x] ==>

x(t) = re^{(M/m)·(v/d)·(1/s)^{2}·t}

w(t) = ( (8/(mdr))·U )^{(1/2)}·(-1)·(m/M)·(d/v)·s^{2}·e^{(-1)·(1/2)·(M/m)·(v/d)·(1/s)^{2}·t}

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mg·d[tx] ==>

x(t) = re^{(M/m)·(g/d)·(1/s)^{2}·(1/2)·t^{2}}

w(t) = ( (8/(mdr))·U )^{(1/2)}·...

... ( (-1)·(m/M)·(d/g)·s^{2}·ln(ut) ) [o(t)o] e^{(-1)·(1/2)·(M/m)·(g/d)·(1/s)^{2}·(1/2)·t^{2}}

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mav·2x·d[x] ==>

x(t) = ( (-1)·(M/m)·(v/d)·(1/s)^{2}·at )^{(-1)}

w(t) = ( (2/(md))·U )^{(1/2)}·( (-1)·(M/m)·(v/d)·(1/s)^{2}·a )^{(1/2)}·(2/3)·t^{(3/2)}

Deducción:

d_{x}[ x^{2} ] = 2x

d_{x}[ x^{2} ]·d[x] = 2x·d[x]

d[ x^{2} ] = 2x·d[x]

L(t) = int[ d[L(t)] ] = int[ (1/s)^{2}·Mav·2x·d[x] ] = ...

... int[ (1/s)^{2}·Mav ]d[x^{2}] =  (1/s)^{2}·Mav·int[ d[x^{2}] ] =  (1/s)^{2}·Mavx^{2}

Ley:

Sea U(w) = U ==>

Si d[L(t)] = (1/s)^{2}·Mag·( d[t]·x^{2}+t·2x·d[x] ) ==>

x(t) = ( (-1)·(M/m)·(g/d)·(1/s)^{2}·a·(1/2)·t^{2} )^{(-1)}

w(t) = ( (2/(md))·U )^{(1/2)}·( (-1)·(M/m)·(g/d)·(1/s)^{2}·a·(1/2) )^{(1/2)}·(1/2)·t^{2}

Deducción:

d_{t}[ tx^{2} ] = d_{t}[t]·x^{2}+t·2x·d_{t}[x]

d_{t}[ tx^{2} ]·d[t] = ( d_{t}[t]·x^{2}+t·2x·d_{t}[x] )·d[t]

d[ tx^{2} ] = d[t]·x^{2}+t·2x·d[x]

L(t) = int[ d[L(t)] ] = int[ (1/s)^{2}·Mag·( d[t]·x^{2}+t·2x·d[x] ) ] = ...

... int[ (1/s)^{2}·Mag ]d[tx^{2}] =  (1/s)^{2}·Mag·int[ d[tx^{2}] ] =  (1/s)^{2}·Magtx^{2}

Ley: [ de rezo al Mal ]

Los hombres no están atacando,

a los xtraterrestres.

Los xtraterrestres no están atacando,

a los hombres.

Ley:

Se matan entre ellos en su mundo.

Cometen adulterio entre ellos en su mundo.

Principio:

U(x,y,z) = Potencial[ Q(x,y,z) ]

U(yz,zx,xy) = Anti-Potencial[ Q(yz,zx,xy) ]

Principio:

div-exp[ U(x,y,z) ] = sum[k = 1]-[3][ d_{xyz}^{3}[ e^{U_{k}(x,y,z)} ]

Si div-exp[ U(x,y,z) ] = 0 ==>

div-exp[ U(x,y,z) ] = d_{xyz}^{3}[ e^{sum[k = 1]-[3][ U_{k}(x,y,z) ]} ]

Principio:

Anti-div-exp[ U(yz,zx,xy) ] = sum[k = 1]-[3][ d_{kij}^{2}[ e^{U_{k}(yz,zx,xy)} ] ]

Si Anti-div-exp[ U(yz,zx,xy) ] = 0 ==>

Anti-div-exp[ U(yz,zx,xy) ] = d_{kij}^{2}[ e^{sum[k = 1]-[3][ U_{k}(yz,zx,xy) ]} ]

Ley:

Si Q(x,y,z) = U·< (1/x),(1/y),(1/z) > ==> 

U(x,y,z) = U·( ln(ax)+ln(ay)+ln(az) )

div-exp[ U(x,y,z) ] = Ua^{3}

F(z) = int-int[ div-exp[ U(x,y,z) ] ]d[x]d[x]+int-int[ div-exp[ U(x,y,z) ] ]d[y]d[y] = ...

... Ua^{3}·(1/2)·( x^{2}+y^{2} )

Ley:

Si Q(yz,zx,xy) = U·< (1/(yz)),(1/(zx)),(1/(xy)) > ==> 

U(yz,zx,xy) = U·( ln(byz)+ln(bzx)+ln(bxy) )

Anti-div-exp[ U(yz,zx,xy) ] = Ub^{3}·4xyz

F(z) = int-int[ Anti-div-exp[ U(yz,zx,xy) ] ]d[x]d[y]+int-int[ Anti-div-exp[ U(yz,zx,xy) ] ]d[y]d[x] = ...

... Ub^{3}·2z·(xy)^{2}

Ley:

Si Q(x,y,z) = aU·< ((y+z)/x),((z+x)/y),((x+y)/z) > ==> 

U(x,y,z) = U·( (ay+az)·ln(ax)+(az+ax)·ln(ay)+(ax+ay)·ln(az) )

div-exp[ U(x,y,z) ] = Ua^{3}·( ...

... (ax)^{ay+az+(-1)}·ln(ax)·( 2+(ay+az)·ln(ax) )+...

... (ay)^{az+ax+(-1)}·ln(ay)·( 2+(az+ax)·ln(ay) )+...

... (az)^{ax+ay+(-1)}·ln(az)·( 2+(ax+ay)·ln(az) ) )

Ley:

E(x_{k}) = int-int[ div-exp[ U_{k}(x,y,z) ] ]d[(1/a)^{2}·(i+j)] = ...

... U·(ak)^{ai+aj+(-1)}·[o(ai+aj)o] ( 2+(1/2)·(ai+aj)·ln(ak) )·(ai+aj)

x_{k}(t) = ...

... (1/a)·Anti-[ ( s /o(s)o/ ...

... int[ (as)^{ai+aj+(-1)}·[o(ai+aj)o] ( 2+(1/2)·(ai+aj)·ln(as) )·(ai+aj) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (2/m)·U )^{(1/2)}·at )

Deducción:

d_{ax}[ (ax)^{ay+az} ] = (ay+az)·(ax)^{ay+az+(-1)} 

d_{ay}[ (ay+az)·(ax)^{ay+az+(-1)} ] = (ax)^{ay+az+(-1)}·( 1+ay·ln(ax)+az·ln(ax) )

d_{az}[ (ax)^{ay+az+(-1)}·( 1+(ay+az)·ln(ax) ) ] = (ax)^{ay+az+(-1)}·ln(ax)·( 2+(ay+az)·ln(ax) )

Ley:

Si Q(yz,zx,xy) = bU·< ((zx+xy)/(yz)),((xy+yz)/(zx)),((yz+zx)/(xy)) > ==> 

U(yz,zx,xy) = U·( (bzx+bxy)·ln(byz)+(bxy+byz)·ln(bzx)+(byz+bzx)·ln(bxy) )

Anti-div-exp[ U(yz,zx,xy) ] = Ub·( ...

... (byz)^{bzx+bxy+(-1)}·(bz+by)·( 1+ln(byz) )+...

... (bzx)^{bxy+byz+(-1)}·(bx+bz)·( 1+ln(bzx) )+...

... (bxy)^{byz+bzx+(-1)}·(by+bx)·( 1+ln(bxy) ) )

Ley:

E(x_{k}) = int[ Anti-div-exp[ U_{k}(yz,zx,xy) ] ]d[(1/b)·k] = U·(bij)^{bik+bkj+(-1)}·( ( 1/ln(bij) )+1 )

x_{k}(t) = (a/b)·Anti-[ ( s /o(s)o/ int[ (bij)^{ais+asj+(-1)}·( ( 1/ln(bij) )+1 ) ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( (2/m)·U )^{(1/2)}·(b/a)·t )

Deducción:

d_{byz}[ (byz)^{bzx+bxy} ] = (bzx+bxy)·(byz)^{bzx+bxy+(-1)}

d_{x}[ (bzx+bxy)·(byz)^{bzx+bxy+(-1)} ] = (byz)^{bzx+bxy+(-1)}·(bz+by)·( 1+ln(byz) )

Áreas y Volumenes:

Teorema:

x = r·cos(w)

y = r·sin(w)

d[x]d[y] = (1/2)·( d[x]d[y]+d[x]d[y] ) = ...

... (1/2)·( d_{r}[x]·d_{w}[y]+(-1)·d_{w}[x]·d_{r}d[y] )·d[r]d[w]

Teorema:

Área de un círculo:

A(r) = int[w = 0]-[2pi][ inr[r = 0]-[r][ r ]d[r] ]d[w] = ...

... int[w = 0]-[2pi][ (1/2)·r^{2} ]d[w] = (1/2)·r^{2}·int[w = 0]-[2pi][ d[w] ] = pi·r^{2}

Perímetro de un círculo:

B(r) = d_{r}[ A(r) ] = d_{r}[ pi·r^{2} ] = 2pi·r

Teorema:

Área de un sector circular:

A(r,w) = int[w = 0]-[w][ inr[r = 0]-[r][ r ]d[r] ]d[w] = ...

... int[w = 0]-[w][ (1/2)·r^{2} ]d[w] = (1/2)·r^{2}·int[w = 0]-[w][ d[w] ] = (1/2)·wr^{2}

Perímetro de un sector circular:

B(r,w) = d_{r}[ A(r,w) ] = d_{r}[ (1/2)·wr^{2} ] = wr

Teorema:

d[z] = r·sin(s)·d[s]

x = r·cos(2w)

y = r·sin(2w)

d[x]d[y]d[z] = (1/2)·( d[x]d[y]d[z]+d[x]d[y]d[z] ) = ...

... (1/2)·( d_{r}[x]·d_{w}[y]+(-1)·d_{w}[x]·d_{r}d[y] )·r·sin(s)·d[r]d[w]d[s] = 

Teorema:

Volumen de una esfera:

A(r) = int[s = 0]-[pi][ int[w = 0]-[2pi][ int[r = 0]-[r][ r^{2}·sin(s) ]d[r] ]d[w] ]d[s] = ...

... int[s = 0]-[pi][ int[w = 0]-[2pi][ (1/3)·r^{3}·sin(s) ]d[w] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·int[w = 0]-[2pi][ d[w] ] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·2pi ]d[s] = (2/3)·pi·r^{3}·int[s = 0]-[pi][ sin(s) ]d[s] = ...

... (2/3)·pi·r^{3}·(-1)·( cos(pi)+(-1)·cos(0) ) = (4/3)·pi·r^{3}

Superficie de una esfera:

B(r) = d_{r}[ A(r) ] = d_{r}[ (4/3)·pi·r^{3} ] = 4pi·r^{2}

Teorema:

Volumen de un hemisferio:

A(r,w) = int[s = 0]-[pi][ int[w = 0]-[w][ int[r = 0]-[r][ r^{2}·sin(s) ]d[r] ]d[w] ]d[s] = ...

... int[s = 0]-[pi][ int[w = 0]-[w][ (1/3)·r^{3}·sin(s) ]d[w] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·int[w = 0]-[w][ d[w] ] ]d[s] = ...

... (1/3)·r^{3}·int[s = 0]-[pi][ sin(s)·w ]d[s] = (2/3)·wr^{3}·int[s = 0]-[pi][ sin(s) ]d[s] = ...

... (2/3)·wr^{3}·(-1)·( cos(pi)+(-1)·cos(0) ) = (2/3)·wr^{3}

Superficie de un hemisferio:

B(r,w) = d_{r}[ A(r,w) ] = d_{r}[ (2/3)·wr^{3} ] = 2wr^{2}

--------------------------------

Mecánica Teórica y Ondas:

--------------------------------

Teorema:

Sea d_{x}[F(x)] = f(x) ==>

d_{x}[ Anti-[F(s)]-(x) ] = ( 1/f( Anti-[F(s)]-(x) ) )

Demostración:

d_{y}[ Anti-[F(s)]-( F(y) ) ] = d_{y}[y] = 1

d[ Anti-[F(s)]-( F(y) ) ] = d[y]

d_{F(y)}[ Anti-[F(s)]-( F(y) ) ] = d_{F(y)}[y] = ( 1/d_{y}[F(y)]) = ( 1/f(y) )

Sea y = Anti-[F(s)]-(x) ==>

d_{F( Anti-[F(s)]-(x) )}[ Anti-[F(s)]-( F( Anti-[F(s)]-(x) ) ) ] = ( 1/f( Anti-[F(s)]-(x) ) )

Teorema:

Sea d_{x}[F(x)] = f(x) ==>

d_{x}[ Anti-[( s /o(s)o/ F(s) )]-(x) ] = f( Anti-[( s /o(s)o/ F(s) )]-(x) )

Demostración:

d_{x}[ Anti-[( s /o(s)o/ F(s) )]-(x) ] = ( 1/( 1/f( Anti-[( s /o(s)o/ F(s) )]-(x) ) ) ) = ...

... f( Anti-[( s /o(s)o/ F(s) )]-(x) )

Teorema:

d_{x}[ arc-sin(x) ] = ( 1/(1+(-1)·x^{2})^{(1/2)} )

Demostración:

d_{x}[ arc-sin(x) ] = ( 1/cos( arc-sin(x) ) ) = ( 1/(1+(-1)·(sin( arc-sin(x) ))^{2})^{(1/2)} )

Teorema:

d_{x}[ arc-cos(x) ] = (-1)·( 1/(1+(-1)·x^{2})^{(1/2)} )

Demostración:

d_{x}[ arc-cos(x) ] = (-1)·( 1/sin( arc-cos(x) ) ) = ( 1/(1+(-1)·(cos( arc-cos(x) ))^{2})^{(1/2)} )

Racionamiento antiguo:

Teorema:

d_{x}[ e^{x} ] = e^{x}

Demostración:

d_{x}[ e^{x} ] = ( 1/(1/y) ) = y = e^{x}

Teorema:

d_{x}[ ln(x) ] = (1/x)

Demostración:

d_{x}[ ln(x) ] = ( 1/e^{y} ) = ( 1/e^{ln(x)} ) = (1/x)

Teorema:

Sea x(t) = Anti-[ ( s /o(s)o/ int[ F(s) ]d[s] )^{[o(s)o] (1/2)} ]-( 2^{(1/2)}·ut ) ] ==>

(1/2)·d_{t}[x(t)]^{2} = F(s)·u^{2}

d_{tt}^{2}[x(t)] = (1/2)·( F(s) )^{(-1)·(1/2)}·f(s)·( F(s) )^{(1/2)}·2u^{2} = f(s)·u^{2}

Demostración:

d_{t}[ F(s) ] = d_{s}[F(s)]·d_{t}[s]

Teorema:

Sea x(t) = Anti-[ ( s /o(s)o/ int[ H(ut) [o(ut)o] F(s) ]d[s] )^{[o(s)o] (1/2)} ]-( 2^{(1/2)}·ut ) ] ==>

(1/2)·d_{t}[x(t)]^{2} = ( H(ut) [o(ut)o] F(s) )·u^{2}

d_{tt}^{2}[x(t)] = ...

... (1/2)·( H(ut) [o(ut)o] F(s) )^{(-1)·(1/2)}·h(ut)·f(s)·( H(ut) [o(ut)o] F(s) )^{(1/2)}·2u^{2} = ...  

... h(ut)·f(s)·u^{2}

Demostración:

u·d_{ut}[ H(ut) [o(ut)o] F(s) ] = u·d_{ut}[H(ut)]·d_{ut}[F(s)] = ...

... u·h(ut)·d_{s}[F(s)]·d_{ut}[s] = h(ut)·d_{s}[F(s)]·d_{t}[s]

Teorema:

Sea x(t) = Anti-[ ( s /o(s)o/ int[ (ut) [o(ut)o] F(s) ]d[s] )^{[o(s)o] (1/2)} ]-( 2^{(1/2)}·ut ) ] ==>

(1/2)·d_{t}[x(t)]^{2} = ( (ut) [o(ut)o] F(s) )·u^{2}

d_{tt}^{2}[x(t)] = ...

... (1/2)·( (ut) [o(ut)o] F(s) )^{(-1)·(1/2)}·f(s)·( (ut) [o(ut)o] F(s) )^{(1/2)}·2u^{2} = f(s)·u^{2}

Ley:

d[H(t)] = (1/pi)^{2}·MgI·d[tx]

x(t) = (1/a)·Anti-[ ( s /o(s)o/ int[ (1/2)·(ut)^{2} [o(ut)o] (1/2)·s^{2} ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( 2·(M/m)·gI·(1/u)·(1/d) )^{(1/2)}·(1/pi)·t )

Deducción:

H(t) = int[ d[H(t)] ] = int[ (1/pi)^{2}·MgI ]d[tx] = (1/pi)^{2}·MgI·int[ d[tx] ] = (1/pi)^{2}·MgItx

md·d_{tt}^{2}[x] = (1/pi)^{2}·MgItx

md·d_{tt}^{2}[x]·d[x] = (1/pi)^{2}·MgI·(1/u)·(ut)·x·d_{ut}[x]·d[ut]

md·(1/2)·d_{t}[ax]^{2} = (1/pi)^{2}·MgI·(1/u)·(1/2)·(ut)^{2} [o(ut)o] (1/2)·(ax)^{2}

Ley:

d[H(t)] = (1/pi)^{2}·Mv·d[(1/t)·x]

x(t) = (1/a)·Anti-[ ( s /o(s)o/ int[ ln(ut) [o(ut)o] (1/2)·s^{2} ]d[s] )^{[o(s)o] (1/2)} ]-( ...

... ( 2·(M/m)·(vu)·(1/d) )^{(1/2)}·(1/pi)·t )

Deducción:

H(t) = int[ d[H(t)] ] = int[ (1/pi)^{2}·Mv ]d[(1/t)·x] = (1/pi)^{2}·Mv·int[ d[(1/t)·x] ] = ...

... (1/pi)^{2}·Mv·(1/t)·x

md·d_{tt}^{2}[x] = (1/pi)^{2}·Mv·(1/t)·x

md·d_{tt}^{2}[x]·d[x] = (1/pi)^{2}·Mvu·(1/(ut))·x·d_{ut}[x]·d[ut]

md·(1/2)·d_{t}[ax]^{2} = (1/pi)^{2}·Mvu·ln(ut) [o(ut)o] (1/2)·(ax)^{2}

Ley:

Le tenéis que decir a Esquerra Republicana,

que queréis el título de la universidad de Stroniken como el mío,

enseñando el testimonio de uno mismo con Dios,

escrito con vuestra letra:

Jûan Garriga Peralta-Peraltotzak:

Filósofo de la ciencia matemática y de la ciencia lógica,

por la universidad de Stroniken.

Y que vos lo envíen.

Ley: [ de onda electro-magnética plana de superficie ]

Lap[ E_{e}(x,y,t) ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ int[ B_{e}(x,y,t) ]d[t] ]

Deducción:

E_{e}(x,y,t)+int[ B_{e}(x,y,t) ]d[t] = 0 = m·d_{tt}^{2}[ < x,y > ]

x(t) = ct·cos(w) 

y(t) = ct·sin(w)

Lap[ int[ B_{e}(x,y,t) ]d[t] ] = ...

... ( 1/(d[x]^{2}+d[y]^{2}) )·(d[x]^{2}+d[y]^{2}) [o] Lap[ int[ B_{e}(x,y,t) ]d[t] ]

Lap[ E_{e}(x,y,t) ]+Lap[ int[ B_{e}(x,y,t) ]d[t] ]= 0^{3}

Lap[ E_{e}(x,y,t) ]+2·(1/c)^{2}·d_{tt}^{2}[ int[ B_{e}(x,y,t) ]d[t] ] = 0^{3}

Lap[ E_{e}(x,y,t) ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ int[ B_{e}(x,y,t) ]d[t] ]

Ley: [ de onda gravito-magnética plana de superficie ]

Lap[ int[ B_{g}(x,y,t) ]d[t] ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ E_{g}(x,y,t) ]

Deducción:

int[ B_{g}(x,y,t) ]d[t]+E_{g}(x,y,t) = 0 = m·d_{tt}^{2}[ < x,y > ]

x(t) = ct·cos(w) 

y(t) = ct·sin(w)

Lap[ E_{g}(x,y,t) ] = ( 1/(d[x]^{2}+d[y]^{2}) )·(d[x]^{2}+d[y]^{2}) [o] Lap[ E_{g}(x,y,t) ]

Lap[ int[ B_{g}(x,y,t) ]d[t] ]+Lap[ E_{g}(x,y,t) ] = 0^{3}

Lap[ int[ B_{g}(x,y,t) ]d[t] ]+2·(1/c)^{2}·d_{tt}^{2}[ E_{g}(x,y,t) ] = 0^{3}

Lap[ int[ B_{g}(x,y,t) ]d[t] ] = (-2)·(1/c)^{2}·d_{tt}^{2}[ E_{g}(x,y,t) ]

Ecuaciones de ondas elípticas planas de superficie:

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = (1/2)·( ...

... e^{ax+ay+acit || ln( H(ax,ay) )+act}+...

... e^{ax+ay+acit || ln( H(ax,ay) )+(-1)·act} )

u(x,y,0) = H(ax,ay)

d_{t}[ u(x,y,0) ] = 0

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·(1/2)·act·0 || (2t)^{(1/2)}]-[h(ax,ay)+(1/2)·act·0 || (2t)^{(1/2)}][ w ]d[w] ]·...

... e^{ax+ay+acit || 0}

u(x,y,0) = 0

d_{t}[ u(x,y,0) ] = ac·h(ax,ay)

Ecuaciones de ondas hiperbólicas planas de superficie:

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = (1/2)·( ...

... e^{ax+ay+act || ln( H(ax,ay) )+act}+...

... e^{ax+ay+act || ln( H(ax,ay) )+(-1)·act} )

u(x,y,0) = H(ax,ay)

d_{t}[ u(x,y,0) ] = 0

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·(1/2)·act·0 || (2t)^{(1/2)}]-[h(ax,ay)+(1/2)·act·0 || (2t)^{(1/2)}][ w ]d[w] ]·...

... e^{ax+ay+act || 0}

u(x,y,0) = 0

d_{t}[ u(x,y,0) ] = ac·h(ax,ay)

Ley:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = E_{e}·(1/2)·( ...

... e^{ax+ay+acit || ln( (ax)^{2}+(ay)^{2} )+act}+...

... e^{ax+ay+acit || ln( (ax)^{2}+(ay)^{2} )+(-1)·act} )

u(x,y,0) = (ax)^{2}+(ay)^{2}

d_{t}[ u(x,y,0) ] = 0

Ley:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,t) = E_{e}·sum[k = 1]-[oo][ ...

... int[(ax+ay)+(-1)·act·0 || (2t)^{(1/2)}]-[(ax+ay)+act·0 || (2t)^{(1/2)}][ w ]d[w] ]·...

... e^{ax+ay+acit || 0}

u(x,y,0) = 0

d_{t}[ u(x,y,0) ] = 2ac·(ax+ay)